ML hw3
Ganbold,MungunSarnai
9/27/2019
Lab Section
In this lab, we will go over regularization, classification and performance metrics. We will be using the caret package in R. https://topepo.github.io/caret/train-models-by-tag.html
Perfomance Metrics
K- fold cross validatation - Resampling method
Randomly split the training data into k folds. If you specify 10 folds, then you split the data into 10 partitions. Train the model on 9 of those partitions, and test your model on the 10th partition. Iterate through until every partition has been held out.
A smaller k is more biased, but a larger k can be very variable.
Bootstrapping - Resampling method
Sample with replacement. Some samples may be represented several times within the boostrap sample, while others may not be represented at all. The samples that are not selected are called out of bag samples.
Boostrap error rates usually have less uncertainty than k-fold cross validation, but higher bias.
Error
Deviation of the observed value to the true value (population mean)
Residual
Deviation of the observed value to the estimated value (sample mean) \[residual=y_i - \hat{y_i}\] where \(\hat{y_i}\) is the estimated value
Mean Squared Error (MSE)
\[MSE=\frac{1}{n}\sum_{i=1}^{n}(y_i - \hat{y_i})^2\]
Root Mean Squared Error (RMSE)
Same units as original data.
\[RMSE=\sqrt{MSE}\]
R^2
Proportion of information explained by the model. It is a measure of correlation, not accuracy. \[1-RSS/TSS\]
L2 regularization : Ridge regression. Regularize by adding the sum of the coefficients, squared, to the function.
\[Ridge Regression=\sum_{i=1}^{n}(y_i - w_0 - \sum_{j=1}^{p}w_jx_{ij})^2 + \lambda\sum_{j=1}^p(w_j)^2\]
L1 regularization : Lasso Regression. Regularize by adding the sum of the absolute value of the coefficients to the model. Coefficient estimates may be pushed to zero – Lasso can perform variable selection
\[Lasso Regression=\sum_{i=1}^{n}(y_i - w_0 - \sum_{j=1}^{p}w_jx_{ij})^2 + \lambda\sum_{j=1}^p|w_j|\]
Sensitivity or True Positive Rate
TP = True Positives TN = True Negatives FP = False Positives - Type I error FN = False Negatives - Type II error N = actual negative samples P = actual positive samples
\[TPR=TP/(TP + FN)\]
Specificity or True Negative Rate
\[TNR=TN/(TN + FP)\]
Receiver Operating Characteristics (ROC)
Plot of True Positive Rate (sensitivity) against False Positive Rate, or plots the True Positive Rate (sensitivity) against specificity.
Either way, a good ROC curves up through the left corner, and has a large area underneath.
Area under ROC curve (AUC)
The area underneath the ROC curve
Logistic function:
\[P(X)=e^{w_0 + w_1X}/{1+e^{w_0+w_1X}}\]
The broad steps of Machine learning in R.
Split the data into training and test. Set test aside.
Fit a good model to the training data. This includes using bootstapping, cross validation etc. to resample the training data and fit a good model.
Visualize if your model learned on the training data by looking at ROC curve and AUC.
Test how your model performs on the test data.
Broad steps for choosing between models according to Max Kuhn and Kjell Johnson
Start with several models that are the least interpretable and the most flexible, like boosted trees and svms. These models are the often the most accurate.
Investigate simpler models that are less opaque, like partial least squares, generalized additive models, or naive bayes models.
Consider using the simplest model that reasonable approximates the performance of more complex models
head(airquality)## Ozone Solar.R Wind Temp Month Day
## 1 41 190 7.4 67 5 1
## 2 36 118 8.0 72 5 2
## 3 12 149 12.6 74 5 3
## 4 18 313 11.5 62 5 4
## 5 NA NA 14.3 56 5 5
## 6 28 NA 14.9 66 5 6Split data into training and test set
train_size <- floor(0.75 * nrow(airquality))
set.seed(543)
train_pos <- sample(seq_len(nrow(airquality)), size = train_size)
train_regression <- airquality[train_pos,-c(1,2)]#remove first two columns
test_regression <- airquality[-train_pos,-c(1,2)]
dim(train_regression) ## [1] 114 4dim(test_regression)## [1] 39 4#train_regression
dim(train_regression)## [1] 114 4Resampling in R
(method = boot, cv, LOOCV …)
?trainControlRidge Regression
\[Ridge Regression=\sum_{i=1}^{n}(y_i - w_0 - \sum_{j=1}^{p}w_jx_{ij})^2 + \lambda\sum_{j=1}^p(w_j)^2\] 2. Create and train model
ctrl = trainControl(method = "boot", 15)
# bootstrapped 15 repititions
Ridge_regression <- train(Temp ~ Wind + Month, data = train_regression,
method = 'ridge', trControl= ctrl) Ridge_regression ## Ridge Regression
##
## 114 samples
## 2 predictor
##
## No pre-processing
## Resampling: Bootstrapped (15 reps)
## Summary of sample sizes: 114, 114, 114, 114, 114, 114, ...
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0e+00 8.185003 0.2868549 6.716834
## 1e-04 8.185000 0.2868560 6.716832
## 1e-01 8.182914 0.2877921 6.715122
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was lambda = 0.1.Examine the residuals
ridge_test_pred <- predict(Ridge_regression, newdata = test_regression)
# plot the predicted values vs the observed values
plot_ridge_test_pred <- data.frame(Temp_test_pred = ridge_test_pred,
Observed_Temp = test_regression$Temp)
#dim(plot_ridge_test_pred)
ggplot(data = plot_ridge_test_pred) +
geom_point(aes(x=Observed_Temp, y = Temp_test_pred)) +
ggtitle("True Temp Value vs Predicted Temp Value Ridge Regression") +
theme_bw()
# median residual value should be close to zero
median(resid(Ridge_regression))## [1] 0.2348498Homework
Lasso
\[Lasso Regression=\sum_{i=1}^{n}(y_i - w_0 - \sum_{j=1}^{p}w_jx_{ij})^2 + \lambda\sum_{j=1}^p|w_j|\] 2. Create and train model
ctrl = trainControl(method = "boot", 9)
# bootstrapped 15 repititions
Lasso_regression <- train(Temp ~ Wind + Month, data = train_regression,
method = 'lasso', trControl= ctrl)Lasso_regression## The lasso
##
## 114 samples
## 2 predictor
##
## No pre-processing
## Resampling: Bootstrapped (9 reps)
## Summary of sample sizes: 114, 114, 114, 114, 114, 114, ...
## Resampling results across tuning parameters:
##
## fraction RMSE Rsquared MAE
## 0.1 8.832033 0.1630620 7.093072
## 0.5 8.242107 0.1968353 6.664605
## 0.9 8.151890 0.2065470 6.556639
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was fraction = 0.9.Examine the residuals (on test):
lasso_test_pred <- predict(Lasso_regression, newdata = test_regression)
# plot the predicted values vs the observed values
plot_lasso_test_pred <- data.frame(Temp_test_pred_lasso = lasso_test_pred,
Observed_Temp = test_regression$Temp)
#dim(plot_lasso_test_pred)
ggplot(data = plot_lasso_test_pred) +
geom_point(aes(x=Observed_Temp, y = Temp_test_pred_lasso)) +
ggtitle("True Temp Value vs Predicted Temp Value Lasso Regression") +
theme_bw()
# median residual value should be close to zero
median(resid(Lasso_regression))## [1] 0.07194436Classification
- Split into training and test set
data(iris)
#split into training and test set
train_size <- floor(0.75 * nrow(iris))
set.seed(543)
train_pos <- sample(seq_len(nrow(iris)), size = train_size)
train_pos## [1] 103 99 113 132 112 104 94 143 60 147 76 5 59 92 111 128 86
## [18] 123 36 77 93 9 21 25 13 138 56 129 87 54 105 65 52 145
## [35] 144 110 95 38 88 72 89 18 140 6 42 7 127 83 14 69 130
## [52] 71 39 20 48 109 51 120 23 97 119 15 27 47 133 17 75 64
## [69] 100 19 117 98 106 40 62 114 43 135 149 150 108 37 67 32 146
## [86] 122 91 3 11 73 96 115 33 22 29 84 30 68 61 55 118 121
## [103] 148 24 10 50 57 53 80 44 34 74#???vector with 117 indexes of randomly sampled train set observations
train_classifier <- iris[train_pos,]
test_classifier <- iris[-train_pos,]
dim(train_classifier) #112x5## [1] 112 5dim(test_classifier) #38x5## [1] 38 5Linear Discriminant analysis
- Good for well separated classes,
- more stable with small n than logistic regression,
- and good for more than 2 response classes.
- LDA assumes a normal distribution with a class specific mean and common variance.
Let’s see if our (unsplitted) data follows the assumptions of LDA.
slength <- ggplot(data = iris, aes(x = Sepal.Length, fill = Species)) +
geom_histogram(position="identity", alpha=0.5, bins= 25) +
ggtitle("Sepal Length by iris species")+
theme_bw()
slength
swidth <- ggplot(data = iris, aes(x = Sepal.Width, fill = Species)) +
geom_histogram(position="identity", alpha=0.5, bins= 25) +
ggtitle("Sepal width by iris species")+
theme_bw()
swidth
plength <- ggplot(data = iris, aes(x = Petal.Length, fill = Species)) +
geom_histogram(position="identity", alpha=0.5, bins= 25) +
ggtitle("Petal lenth by iris species")+
theme_bw()
plength
pwidth <- ggplot(data = iris, aes(x = Petal.Width, fill = Species)) +
geom_histogram(position="identity", alpha=0.5, bins= 25) +
ggtitle("Petal width by iris species")+
theme_bw()
pwidth
grid.arrange(slength, swidth, plength, pwidth)
Note Conclusion on LDA suitability check with Xj histograms: n is rather small each level of response distribution is close to normal more than 2 levels of response Y well separated classes?..
LDA analysis on train set:
Note: lda(y~ x1+x2…, data, cv=T)
LDA <- lda(Species~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width,
data= train_classifier, cv= T)
LDA## Call:
## lda(Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width,
## data = train_classifier, cv = T)
##
## Prior probabilities of groups:
## setosa versicolor virginica
## 0.3214286 0.3571429 0.3214286
##
## Group means:
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## setosa 5.002778 3.441667 1.441667 0.2472222
## versicolor 5.975000 2.802500 4.297500 1.3425000
## virginica 6.625000 2.961111 5.602778 2.0166667
##
## Coefficients of linear discriminants:
## LD1 LD2
## Sepal.Length 0.8688807 0.0250930
## Sepal.Width 1.3090031 2.2033404
## Petal.Length -2.1733913 -0.9306213
## Petal.Width -2.9542135 2.9217844
##
## Proportion of trace:
## LD1 LD2
## 0.9925 0.0075Note Conclusion of LDA: * ‘LDA probabilities of groups’ shows ~equally represented class/response levels * ‘Group means’ ?????? Xj not really normally distributed * ‘Proportion of trace’ - percentage separation achieved by each discriminant function.Number of discriminant functions=(j-1), where j is a number levels in the response. Therefore, in LDA j>2.
!LD1 function is the best to explain the data variance. Sepal.length and Sepal.width are the two variables with positive strong relationship with this function.
- Test model on test set
#predict the species of the test data
LDA_predict <- predict(LDA, newdata=test_classifier)
LDA_predict## $class
## [1] setosa setosa setosa setosa setosa setosa
## [7] setosa setosa setosa setosa setosa setosa
## [13] setosa setosa versicolor versicolor versicolor versicolor
## [19] versicolor versicolor versicolor versicolor versicolor versicolor
## [25] virginica virginica virginica virginica virginica virginica
## [31] virginica virginica versicolor virginica virginica virginica
## [37] virginica virginica
## Levels: setosa versicolor virginica
##
## $posterior
## setosa versicolor virginica
## 1 1.000000e+00 8.927588e-22 1.502714e-42
## 2 1.000000e+00 5.608958e-18 7.859057e-38
## 4 1.000000e+00 1.340664e-16 8.780825e-36
## 8 1.000000e+00 7.063790e-20 4.874210e-40
## 12 1.000000e+00 3.071910e-18 9.278990e-38
## 16 1.000000e+00 2.450746e-26 1.808054e-47
## 26 1.000000e+00 1.741777e-16 8.142385e-36
## 28 1.000000e+00 3.298574e-21 8.515021e-42
## 31 1.000000e+00 2.177639e-16 1.541993e-35
## 35 1.000000e+00 1.139046e-17 2.613655e-37
## 41 1.000000e+00 3.067677e-21 1.548311e-41
## 45 1.000000e+00 8.513016e-17 6.298481e-35
## 46 1.000000e+00 1.619854e-16 1.480553e-35
## 49 1.000000e+00 8.466069e-23 8.730428e-44
## 58 1.428152e-13 1.000000e+00 3.990264e-08
## 63 2.374740e-17 9.999997e-01 3.470145e-07
## 66 2.056260e-17 9.999767e-01 2.334426e-05
## 70 4.162354e-17 9.999987e-01 1.266945e-06
## 78 5.219725e-27 7.577590e-01 2.422410e-01
## 79 3.553343e-23 9.952595e-01 4.740522e-03
## 81 3.715969e-17 9.999989e-01 1.097426e-06
## 82 3.965139e-15 9.999999e-01 1.096980e-07
## 85 1.036329e-24 9.716164e-01 2.838356e-02
## 90 1.350592e-20 9.999173e-01 8.267215e-05
## 101 5.859828e-53 3.814340e-09 1.000000e+00
## 102 5.479761e-38 1.245695e-03 9.987543e-01
## 107 5.707472e-33 6.378269e-02 9.362173e-01
## 116 8.008099e-41 1.986249e-05 9.999801e-01
## 124 3.240609e-31 1.348781e-01 8.651219e-01
## 125 4.511111e-40 7.110302e-05 9.999289e-01
## 126 9.318183e-37 2.895450e-03 9.971045e-01
## 131 9.974593e-42 1.875211e-04 9.998125e-01
## 134 2.332648e-28 8.097276e-01 1.902724e-01
## 136 8.719380e-46 2.112584e-06 9.999979e-01
## 137 2.102117e-45 5.219049e-07 9.999995e-01
## 139 2.649695e-29 2.178681e-01 7.821319e-01
## 141 1.371274e-45 9.014290e-07 9.999991e-01
## 142 1.702640e-36 4.062736e-04 9.995937e-01
##
## $x
## LD1 LD2
## 1 8.09659797 0.24247894
## 2 7.26832029 -0.86420986
## 4 6.92121725 -0.74446585
## 8 7.66147047 -0.07342653
## 12 7.27035519 -0.17150726
## 16 8.98784735 2.73183587
## 26 6.92053011 -1.04782483
## 28 7.96614692 0.15192611
## 31 6.87765427 -0.83250938
## 35 7.18188147 -0.73693795
## 41 7.93162767 0.62521022
## 45 6.81176056 1.02252730
## 46 6.88601087 -0.57454072
## 49 8.31483561 0.59510349
## 58 -0.00989576 -1.61696704
## 63 -0.83730146 -2.68146774
## 66 -1.10202409 0.11556898
## 70 -0.87023505 -1.64526224
## 78 -3.42322321 0.21339749
## 79 -2.48480169 -0.14354788
## 81 -0.87068430 -1.77504345
## 82 -0.35792383 -1.97415976
## 85 -2.87522982 0.06173036
## 90 -1.76530495 -1.15647678
## 101 -7.91483665 2.27116866
## 102 -5.40609861 0.02110643
## 107 -4.55501442 -0.46812946
## 116 -5.84663229 2.12042195
## 124 -4.24155864 -0.07240126
## 125 -5.73358157 1.39167848
## 126 -5.19579484 0.02816921
## 131 -6.05838040 -0.64903204
## 134 -3.65907254 -0.91472681
## 136 -6.71760097 0.96787771
## 137 -6.61915848 2.57157278
## 139 -3.89218282 0.67413510
## 141 -6.66430711 1.92060786
## 142 -5.10841398 2.09875866Notes (https://www.displayr.com/linear-discriminant-analysis-in-r-an-introduction/):
LDA OUTPUT FOR VALIDATION SET:
$class - shows actual class level (in validation set)
$posterior - is the regressional weight for each indexed observation in validation set. The highest score predicts the sub-class.
ONE CAN COMPARE class=actual vs. posterior=predicted (in valid.set)
*2 LD functions are run parallely for each n. Mean LD1 and LD2 (for each n) is calculated next and the best LD function is selected (‘LD trace’. Tracing that LD one can see the features strongly correlated with it) .
3(=Yj) mean d.scores are collected for each feature (Xi). It will be a df [j:i]. The highest disc score will reveal the ‘j’ sub-class prediction. R^2 correlation coefficient is calculated for this prediction. All R^2 scores are collected (one for each feature, a vector with i length). The highest R^2 score identifies the discriminating attribute.
Thus, LDA is not only a supervised classifing method but also a dimension reduction technique as well (for not large n sample with independent and normally distr-ed Xi and Yj>2).
$x LD1 and LD2 -linear discriminants (remember that in this case with 3 classes we have at most two linear discriminants) are combination coefficients for each of indexed observation in validation set.
**** $singular values (svd) - gives the ratio of the between- and within-group standard deviations on the linear discriminant variables (LDs). {not shown in this output} ***** $prop -We can use the singular values to compute the amount of the between-group variance that is explained by each linear discriminant. In our example we see that the first linear discriminant explains more than {99%} of the between-group variance in the iris dataset. {not shown in this output}
Confusion Matrix A confusion matrix is a technique for summarizing the performance of a classification algorithm. Classification accuracy alone can be misleading if you have an unequal number of observations in each class or if you have more than two classes in your dataset.
#?confusionMatrix()#install.packages("e1071")
confusionMatrix(LDA_predict$class, reference = test_classifier$Species)## Confusion Matrix and Statistics
##
## Reference
## Prediction setosa versicolor virginica
## setosa 14 0 0
## versicolor 0 10 1
## virginica 0 0 13
##
## Overall Statistics
##
## Accuracy : 0.9737
## 95% CI : (0.8619, 0.9993)
## No Information Rate : 0.3684
## P-Value [Acc > NIR] : 2.196e-15
##
## Kappa : 0.9603
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: setosa Class: versicolor Class: virginica
## Sensitivity 1.0000 1.0000 0.9286
## Specificity 1.0000 0.9643 1.0000
## Pos Pred Value 1.0000 0.9091 1.0000
## Neg Pred Value 1.0000 1.0000 0.9600
## Prevalence 0.3684 0.2632 0.3684
## Detection Rate 0.3684 0.2632 0.3421
## Detection Prevalence 0.3684 0.2895 0.3421
## Balanced Accuracy 1.0000 0.9821 0.9643- kappa - or Cohen’s coefficient is similar to correlation coefficients, it can range from −1 to +1, where 0 represents the amount of agreement that can be expected from random chance, and 1 represents perfect agreement between the raters. While kappa values below 0 are possible, Cohen notes they are unlikely in practice
#Activation function maps Pred.score [-int:+int] to Probability (0 of PS mamps to 0.5 of Prob. Max of PS maps to max of Prob.=1, same for the mins.)
# LDA_predict$posterior = df[idx:PredScore for each 3Species] = df[38:3], where index is not incl in the dataframe
# save the predictions in a new variable
predictions <- as.data.frame(LDA_predict$posterior) %>%
rownames_to_column("idx") # rownames (indexes of validation set) are now officialy under column name 'idx' and are included in df. The df is now one column bigger = [38:4]
test_classifier <- test_classifier %>%
rownames_to_column("idx")
#now test_classifier has officially Index as a row name.
#df[38:5] became [38:6]
predictions_actual <- full_join(predictions,test_classifier, by = "idx" ) #join and order by Index
#predictions =df[38:4]. Idx;regression weight for 3 sub-classesY1-3
#predictions_actual=df[38:9]. Idx,predicted RWeights for all Y1-3, actual X1-4, actual_Y class
# choose the two classes we want to compare, setosa and versicolor
set_vers_true_labels <- predictions_actual %>%
filter(Species %in% c("setosa", "versicolor")) %>%
#[24:9] filtered 24 obs where Y1 or Y2 have the discriminating PredScore (all observations with high PredSc for Y3 is not here)
mutate(Species = as.character(Species))
#(df[24:9]; idx, PredScore for Y1-3 (where Y3 score is never discr-ve), actual X1-4, actual_class for these 24 predictions)
#make dataframe PredScores for setosa and the actual labels
pred_label <- data.frame(prediction = set_vers_true_labels$setosa,
label = set_vers_true_labels$Species)
#df[24:2]
# summary of prediction:
ggplot(pred_label, aes(x = 1:24, y = prediction, color = label))+
geom_point()+
ggtitle("Prediction Scores calculated for Setosa in test set are mapped to\n probabilities using activating function. As a result,in test set, 14\n observations were\n predicted by LDA as setosa and 10 were predicted as versicolor.")
pred <- prediction(set_vers_true_labels$setosa, set_vers_true_labels$Species,
label.ordering = c("versicolor", "setosa"))
#24 filtered PredScores for setosa column are presented in df.
#Positive/high PredScores are marked as 'setosa', otherwise, obs. with negative scores labeled as 'versicolor') (Levels: versicolor < setosa)
#Also, outputs for cutoff 'n' TP, TN, FP, FN and more.
#ROC Curve:
perf <- performance(pred,"tpr","fpr")
plot(perf, main="ROC curve for LDA prediction of setosa class:\n sensitivity vs specificty", col = "red")
Logistic Regression
\(logodds_i=B_0 + B_1X_{i1}\)
Here, the log odds represents the log odds of \(Y_i\) being 0 or 1.
Where \(logodds\) is the dependent variable, and \(X_i\) is the independent variable. \(B_{number}\) are the parameters to fit.
Logistic Regression assumes a linear relationship between the \(logodds\) and \(X\).
To convert from logodds, a not intuitive quantity, to odds, a more intuitive quantity, we use this non-linear equation:
\(odds_i=e^{logodds_{i}}\) or \(odds_i=e^{B_0 + B_1X_{i1}}\)
Odds is defined as the probability that the event will occur divided by the probability that the event will not occur.
Now we convert from odds to probability.
The probability that an event will occur is the fraction of times you expect to see that event in many trials. Probabilities always range between 0 and 1.
To convert from odds to a probability, divide the odds by one plus the odds. So to convert odds of 1/9 to a probability, divide 1/9 by 10/9 to obtain the probability of 0.10
Note: odds=a/b probty=a/(a+b)
odds <- e^(log_odds)
\(P=odds/(odds+1)\)
Logistic Regression implementation
- Y=1 is the probability of the event occuring.
- Independent variables should not be correlated.
- Log odds and independent variables should be linearly correlated.
- Train and fit model
data(iris)
#split into training and test set
train_size <- floor(0.75 * nrow(iris))
set.seed(543)
train_pos <- sample(seq_len(nrow(iris)), size = train_size)
train_classifier <- iris[train_pos,]
test_classifier <- iris[-train_pos,]
dim(train_classifier) #[11:5]## [1] 112 5dim(test_classifier) #[38:5]## [1] 38 5#Preparing data for Logistic Regression
#only look at two classes in each of data chunck:
train_classifier_log <- train_classifier[c(which(train_classifier$Species == "setosa"),
which(train_classifier$Species == "versicolor")),]
test_classifier_log <- test_classifier[c(which(test_classifier$Species == "setosa"),
which(test_classifier$Species == "versicolor")),]
#Stashing away Predictors for each data chunck:
train_classifier_log$Species <- factor(train_classifier_log$Species)
test_classifier_log$Species <- factor(test_classifier_log$Species)
#Setting up control parameters for fitting Logistic Regression:
ctrl <- trainControl(method = "repeatedcv", repeats = 15,classProbs = T,
savePredictions = T)
#summary(ctrl)
#create model. logistic regression is a bionomial general linear model.
#predict species based on sepal length with set up control
logistic_regression <- train(Species~ Sepal.Length, data = train_classifier_log,
method = "glm", family= "binomial", trControl = ctrl)logistic_regression## Generalized Linear Model
##
## 76 samples
## 1 predictor
## 2 classes: 'setosa', 'versicolor'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 15 times)
## Summary of sample sizes: 68, 68, 68, 69, 69, 68, ...
## Resampling results:
##
## Accuracy Kappa
## 0.8897619 0.7782065kappa is a coefficient of agreement, ranges [-1;+1]. 0=random chance. is rarely negative.
summary(logistic_regression)##
## Call:
## NULL
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.02223 -0.45039 0.03625 0.41197 2.16274
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -28.134 6.377 -4.412 1.02e-05 ***
## Sepal.Length 5.179 1.172 4.419 9.93e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 105.15 on 75 degrees of freedom
## Residual deviance: 46.67 on 74 degrees of freedom
## AIC: 50.67
##
## Number of Fisher Scoring iterations: 6- Visualize ROC curve
plot(x = roc(predictor = logistic_regression$pred$setosa,
response = logistic_regression$pred$obs)$specificities,
y = roc(predictor = logistic_regression$pred$setosa,
response = logistic_regression$pred$obs)$sensitivities,
col= "blue", xlim = c(1, 0), type ="l", ylab = "Sensitivity",
xlab = "Specificity")## Setting levels: control = setosa, case = versicolor## Setting direction: controls > cases## Setting levels: control = setosa, case = versicolor## Setting direction: controls > caseslegend("bottomright", legend = paste("setosa v versicolor --",
roc(predictor = logistic_regression$pred$setosa,
response = logistic_regression$pred$obs)$auc
, sep = ""), col = c("blue"), fill = c("blue"))## Setting levels: control = setosa, case = versicolor
## Setting direction: controls > cases
- Test on an independent set
#predict iris species using Sepal legth
logistic_regression_predict_class <- predict(logistic_regression,
newdata = test_classifier_log)
#confusion matrix
confusionMatrix(logistic_regression_predict_class,
reference = test_classifier_log$Species)## Confusion Matrix and Statistics
##
## Reference
## Prediction setosa versicolor
## setosa 13 2
## versicolor 1 8
##
## Accuracy : 0.875
## 95% CI : (0.6764, 0.9734)
## No Information Rate : 0.5833
## P-Value [Acc > NIR] : 0.002161
##
## Kappa : 0.7391
##
## Mcnemar's Test P-Value : 1.000000
##
## Sensitivity : 0.9286
## Specificity : 0.8000
## Pos Pred Value : 0.8667
## Neg Pred Value : 0.8889
## Prevalence : 0.5833
## Detection Rate : 0.5417
## Detection Prevalence : 0.6250
## Balanced Accuracy : 0.8643
##
## 'Positive' Class : setosa
## ! Check if log odds and independent variables are linearly correlated
#Probability for each event for each class:
logistic_regression_predict <- predict(logistic_regression,
newdata = test_classifier_log, type = "prob") #df[testset:2(Y1 and Y2)]
# To convert from a probability to odds, divide the probability by one minus that probability. So if the probability is 10% or 0.10 , then the odds are 0.1/0.9 or ‘1 to 9’
odds_species1 <- logistic_regression_predict[,1] / (1 - logistic_regression_predict[,1])
log_odds_species1 <- log(odds_species1)
#log_odds and indep.variable X must be linearly correlated:
cor.test(log_odds_species1, test_classifier_log$Sepal.Length)##
## Pearson's product-moment correlation
##
## data: log_odds_species1 and test_classifier_log$Sepal.Length
## t = -Inf, df = 22, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -1 -1
## sample estimates:
## cor
## -1plot(log_odds_species1, test_classifier_log$Sepal.Length)
Look deeper at the logistic regression
#Again, probability for each event for 2 classes:
logistic_predict_prob <- predict(logistic_regression,
newdata = test_classifier_log, type="prob") #df[90:2]
#prepare df to plot = predicted + actual labels:
logistic_pred_prob_plot <- data.frame(Species_pred = logistic_predict_prob, Sepal.Length = test_classifier_log$Sepal.Length)
#Stash away actual labels as numeric (as logical vector):
test_classifier_log$Species <- as.numeric(test_classifier_log$Species) -1
# Plotting predictions and actual observations
ggplot(data = test_classifier_log) +
geom_point(aes(x=Sepal.Length, y = Species)) +
geom_line(data = logistic_pred_prob_plot, aes(x = Sepal.Length,
y = Species_pred.setosa, col = "setosa"))+
geom_line(data = logistic_pred_prob_plot, aes(x = Sepal.Length,
y = Species_pred.versicolor, col = "versicolor"))+
ggtitle("Probabilities for classifying species")
#Homework:
- Use the Breast Cancer dataset from the mlbench package, and predict whether the cancer is malignant or benign using one of the algorithms we learned about in class. Give some rationale as to why you chose this algorithm. Plot ROC curves, and confusion matrices. If you are choosing a hyperparameter like K or lambda, explain how and why you chose it.
Downloading data:
#install.packages("mlbench")
library(mlbench)
data(BreastCancer)
head(BreastCancer)## Id Cl.thickness Cell.size Cell.shape Marg.adhesion Epith.c.size
## 1 1000025 5 1 1 1 2
## 2 1002945 5 4 4 5 7
## 3 1015425 3 1 1 1 2
## 4 1016277 6 8 8 1 3
## 5 1017023 4 1 1 3 2
## 6 1017122 8 10 10 8 7
## Bare.nuclei Bl.cromatin Normal.nucleoli Mitoses Class
## 1 1 3 1 1 benign
## 2 10 3 2 1 benign
## 3 2 3 1 1 benign
## 4 4 3 7 1 benign
## 5 1 3 1 1 benign
## 6 10 9 7 1 malignantstr(BreastCancer)## 'data.frame': 699 obs. of 11 variables:
## $ Id : chr "1000025" "1002945" "1015425" "1016277" ...
## $ Cl.thickness : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 5 5 3 6 4 8 1 2 2 4 ...
## $ Cell.size : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 1 4 1 8 1 10 1 1 1 2 ...
## $ Cell.shape : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 1 4 1 8 1 10 1 2 1 1 ...
## $ Marg.adhesion : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 1 5 1 1 3 8 1 1 1 1 ...
## $ Epith.c.size : Ord.factor w/ 10 levels "1"<"2"<"3"<"4"<..: 2 7 2 3 2 7 2 2 2 2 ...
## $ Bare.nuclei : Factor w/ 10 levels "1","2","3","4",..: 1 10 2 4 1 10 10 1 1 1 ...
## $ Bl.cromatin : Factor w/ 10 levels "1","2","3","4",..: 3 3 3 3 3 9 3 3 1 2 ...
## $ Normal.nucleoli: Factor w/ 10 levels "1","2","3","4",..: 1 2 1 7 1 7 1 1 1 1 ...
## $ Mitoses : Factor w/ 9 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 5 1 ...
## $ Class : Factor w/ 2 levels "benign","malignant": 1 1 1 1 1 2 1 1 1 1 ...#is.na(BreastCancer) # couple of NA in $Bare.nuclei
dim(BreastCancer)## [1] 699 11BreastCancer_clean<- na.omit(BreastCancer)
is.na(BreastCancer_clean)## Id Cl.thickness Cell.size Cell.shape Marg.adhesion Epith.c.size
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## Bare.nuclei Bl.cromatin Normal.nucleoli Mitoses Class
## 1 FALSE FALSE FALSE FALSE FALSE
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## 619 FALSE FALSE FALSE FALSE FALSE
## 620 FALSE FALSE FALSE FALSE FALSE
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## 624 FALSE FALSE FALSE FALSE FALSE
## 625 FALSE FALSE FALSE FALSE FALSE
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## 627 FALSE FALSE FALSE FALSE FALSE
## 628 FALSE FALSE FALSE FALSE FALSE
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## 630 FALSE FALSE FALSE FALSE FALSE
## 631 FALSE FALSE FALSE FALSE FALSE
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## 634 FALSE FALSE FALSE FALSE FALSE
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## 637 FALSE FALSE FALSE FALSE FALSE
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## 640 FALSE FALSE FALSE FALSE FALSE
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## 651 FALSE FALSE FALSE FALSE FALSE
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## 655 FALSE FALSE FALSE FALSE FALSE
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## 669 FALSE FALSE FALSE FALSE FALSE
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## 681 FALSE FALSE FALSE FALSE FALSE
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## 696 FALSE FALSE FALSE FALSE FALSE
## 697 FALSE FALSE FALSE FALSE FALSE
## 698 FALSE FALSE FALSE FALSE FALSE
## 699 FALSE FALSE FALSE FALSE FALSEdim(BreastCancer_clean) [683:11]## [1] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [24] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [47] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [70] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [93] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [116] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [139] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [162] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [185] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [208] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [231] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [254] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [277] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [300] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [323] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [346] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [369] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [392] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [415] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [438] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [461] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [484] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [507] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [530] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [553] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [576] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [599] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [622] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [645] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [668] NA NA NA NA NA NAsummary(BreastCancer_clean$Class)## benign malignant
## 444 239Data:
n=699, after NA ommited, n=683 9 variables - ordinary numbers with 10 or 9 levels each 458-B and 241-M. After cleaning, predictor’s 2 classes:444-B and 239-M
The main goal of this task is to find a function to classify accurately predictor’s 2 classes.
Method chosen is Dimension Reduction with Multiple Correspondence Analysis and Logistic Regression build on selected dimension/features:
- Since the variables are all categorical, I will use MCA as a dimension reduction technique. MCA enables the study of both the relationship between the observations and the associations between variable categories (biplot).
{The other technique for me to try is ‘latent class analysis in R’ next time.}
{If I had more than two classes, I would have considered LDA as linear classification and DR method for categorical data.}
- MCA raw coordinates from selected dimension(s) will serve as a new predictor for Logistic Regression on train set to build the classification model. Afterwards, the model will be validated on test set.
3.Depending on the model performance (ROC and AUC), I might proceed for L1 and L2 regularizations.
1. Multiple Correspondence Analysis (MCA) for categ.variables without predictor:
(http://www.sthda.com/english/wiki/print.php?id=232#variable-categories)
data(BreastCancer_clean)## Warning in data(BreastCancer_clean): data set 'BreastCancer_clean' not
## foundhead( BreastCancer_MCA<- BreastCancer_clean[, 2:10]) #excl.Ind and Class## Cl.thickness Cell.size Cell.shape Marg.adhesion Epith.c.size Bare.nuclei
## 1 5 1 1 1 2 1
## 2 5 4 4 5 7 10
## 3 3 1 1 1 2 2
## 4 6 8 8 1 3 4
## 5 4 1 1 3 2 1
## 6 8 10 10 8 7 10
## Bl.cromatin Normal.nucleoli Mitoses
## 1 3 1 1
## 2 3 2 1
## 3 3 1 1
## 4 3 7 1
## 5 3 1 1
## 6 9 7 1Data: Plotting the frequency of variable categories:
for (i in 1:ncol(BreastCancer_MCA)) {
plot(BreastCancer_MCA[,i], main=colnames(BreastCancer_MCA)[i],
ylab = "Count", col="steelblue", las = 2)
}
*Optional: Histogram of variable counts (though I am not using LDA here)
cellsize <- ggplot(data = BreastCancer_clean, aes(x = as.numeric(Cell.size), fill = Class)) +
geom_histogram(position="identity", alpha=0.5, bins= 25) +
ggtitle("Cell size by Class (B/M)")+
theme_bw()
cellsize
cellshape <- ggplot(data = BreastCancer_clean, aes(x = as.numeric(Cell.shape), fill = Class)) +
geom_histogram(position="identity", alpha=0.5, bins= 25) +
ggtitle("Cell shape by Class (B/M)")+
theme_bw()
cellshape
grid.arrange(cellsize, cellshape)
####MCA: FactoMineR::MCA() (by default: MCA(X, ncp = 5, graph = TRUE)) X : a data frame with n rows (individuals) and p columns (categorical variables) ncp : number of dimensions kept in the final results. graph : a logical value. If TRUE a graph is displayed.
(guidance from: https://r.789695.n4.nabble.com/How-to-use-PC1-of-PCA-and-dim1-of-MCA-as-a-predictor-in-logistic-regression-model-for-data-reduction-td3750251.html)
#Then, I used mjca of ca pacakge for MCA.
#install.packages("ca")
library(ca)
mjca1 <- mjca(BreastCancer_MCA)
summary(mjca1) ##
## Principal inertias (eigenvalues):
##
## dim value % cum% scree plot
## 1 0.470641 65.8 65.8 *******************
## 2 0.050913 7.1 72.9 **
## 3 0.018727 2.6 75.5 *
## 4 0.012462 1.7 77.2
## 5 0.011066 1.5 78.8
## 6 0.009880 1.4 80.2
## 7 0.008198 1.1 81.3
## 8 0.007278 1.0 82.3
## 9 0.006711 0.9 83.3
## 10 0.005891 0.8 84.1
## 11 0.004856 0.7 84.8
## 12 0.004246 0.6 85.4
## 13 0.003943 0.6 85.9
## 14 0.003128 0.4 86.3
## 15 0.002650 0.4 86.7
## 16 0.002494 0.3 87.1
## 17 0.001875 0.3 87.3
## 18 0.001701 0.2 87.6
## 19 0.001434 0.2 87.8
## 20 0.001263 0.2 87.9
## 21 0.001111 0.2 88.1
## 22 0.000991 0.1 88.2
## 23 0.000653 0.1 88.3
## 24 0.000525 0.1 88.4
## 25 0.000448 0.1 88.5
## 26 0.000254 0.0 88.5
## 27 0.000186 0.0 88.5
## 28 0.000154 0.0 88.5
## 29 9.4e-050 0.0 88.6
## 30 5.7e-050 0.0 88.6
## 31 5.5e-050 0.0 88.6
## 32 3e-05000 0.0 88.6
## 33 1.4e-050 0.0 88.6
## -------- -----
## Total: 0.715685
##
##
## Columns:
## name mass qlt inr k=1 cor ctr k=2 cor ctr
## 1 | Cl.thickness:1 | 23 952 11 | 617 937 18 | 79 15 3 |
## 2 | Cl.thickness:2 | 8 812 9 | 524 811 5 | 21 1 0 |
## 3 | Cl.thickness:3 | 17 816 8 | 400 805 6 | -48 11 1 |
## 4 | Cl.thickness:4 | 13 689 8 | 360 686 4 | -24 3 0 |
## 5 | Cl.thickness:5 | 21 30 7 | -43 30 0 | 0 0 0 |
## 6 | Cl.thickness:6 | 5 489 9 | -561 478 4 | 83 11 1 |
## 7 | Cl.thickness:7 | 4 699 11 | -1032 529 8 | -583 169 25 |
## 8 | Cl.thickness:8 | 7 786 13 | -1042 785 17 | -22 0 0 |
## 9 | Cl.thickness:9 | 2 517 11 | -1088 472 6 | 335 45 5 |
## 10 | Cl.thickness:10 | 11 903 14 | -1060 903 27 | 26 1 0 |
## 11 | Cell.size:1 | 61 952 17 | 612 942 48 | 64 10 5 |
## 12 | Cell.size:2 | 7 270 9 | 297 202 1 | -172 68 4 |
## 13 | Cell.size:3 | 8 404 9 | -218 93 1 | -400 311 27 |
## 14 | Cell.size:4 | 6 588 12 | -764 418 8 | -487 170 29 |
## 15 | Cell.size:5 | 5 624 13 | -1076 550 12 | -394 74 15 |
## 16 | Cell.size:6 | 4 561 12 | -1011 502 9 | -346 59 10 |
## 17 | Cell.size:7 | 3 538 12 | -1137 523 8 | -194 15 2 |
## 18 | Cell.size:8 | 5 562 13 | -1109 550 12 | -167 13 3 |
## 19 | Cell.size:9 | 1 324 10 | -1240 321 3 | -116 3 0 |
## 20 | Cell.size:10 | 11 892 21 | -1247 638 36 | 787 254 133 |
## 21 | Cell.shape:1 | 56 953 16 | 622 942 46 | 68 11 5 |
## 22 | Cell.shape:2 | 9 274 9 | 294 231 2 | -128 44 3 |
## 23 | Cell.shape:3 | 9 230 8 | -83 25 0 | -240 205 10 |
## 24 | Cell.shape:4 | 7 526 11 | -595 389 5 | -354 137 17 |
## 25 | Cell.shape:5 | 5 640 12 | -896 523 9 | -423 117 18 |
## 26 | Cell.shape:6 | 5 634 12 | -925 507 9 | -464 128 20 |
## 27 | Cell.shape:7 | 5 657 13 | -1148 586 14 | -397 70 15 |
## 28 | Cell.shape:8 | 4 577 12 | -1106 575 11 | 70 2 0 |
## 29 | Cell.shape:9 | 1 321 10 | -1078 321 3 | 31 0 0 |
## 30 | Cell.shape:10 | 9 894 21 | -1289 627 33 | 841 267 131 |
## 31 | Marg.adhesion:1 | 64 991 13 | 522 986 37 | 36 5 2 |
## 32 | Marg.adhesion:2 | 9 183 8 | -71 28 0 | -166 154 5 |
## 33 | Marg.adhesion:3 | 9 363 8 | -257 285 1 | -134 77 3 |
## 34 | Marg.adhesion:4 | 5 735 11 | -788 515 7 | -515 220 28 |
## 35 | Marg.adhesion:5 | 4 661 11 | -1057 596 9 | -351 66 9 |
## 36 | Marg.adhesion:6 | 3 605 10 | -874 555 6 | -261 50 5 |
## 37 | Marg.adhesion:7 | 2 457 12 | -1327 440 8 | 257 17 3 |
## 38 | Marg.adhesion:8 | 4 689 12 | -1193 661 12 | 242 27 5 |
## 39 | Marg.adhesion:9 | 1 198 9 | -889 198 1 | -21 0 0 |
## 40 | Marg.adhesion:10 | 9 846 17 | -1212 746 28 | 443 100 35 |
## 41 | Epith.c.size:1 | 7 846 9 | 641 826 6 | 100 20 1 |
## 42 | Epith.c.size:2 | 61 980 13 | 540 979 38 | 17 1 0 |
## 43 | Epith.c.size:3 | 12 661 10 | -436 361 5 | -398 300 36 |
## 44 | Epith.c.size:4 | 8 792 12 | -912 692 14 | -346 99 18 |
## 45 | Epith.c.size:5 | 6 692 12 | -978 672 13 | -168 20 4 |
## 46 | Epith.c.size:6 | 7 806 13 | -1082 774 16 | 222 33 6 |
## 47 | Epith.c.size:7 | 2 483 11 | -1220 462 6 | 260 21 2 |
## 48 | Epith.c.size:8 | 3 638 11 | -1096 589 9 | 318 50 7 |
## 49 | Epith.c.size:9 | 0 180 10 | -1451 141 1 | 762 39 4 |
## 50 | Epith.c.size:10 | 5 817 13 | -1149 611 14 | 667 206 44 |
## 51 | Bare.nuclei:1 | 65 982 14 | 550 973 42 | 52 9 3 |
## 52 | Bare.nuclei:2 | 5 9 8 | -49 8 0 | -17 1 0 |
## 53 | Bare.nuclei:3 | 5 241 9 | -242 118 1 | -247 123 5 |
## 54 | Bare.nuclei:4 | 3 318 9 | -557 318 2 | -14 0 0 |
## 55 | Bare.nuclei:5 | 5 516 9 | -610 514 4 | -30 1 0 |
## 56 | Bare.nuclei:6 | 1 104 10 | -761 103 1 | 70 1 0 |
## 57 | Bare.nuclei:7 | 1 371 10 | -938 232 2 | -725 139 13 |
## 58 | Bare.nuclei:8 | 3 522 11 | -996 509 7 | -159 13 2 |
## 59 | Bare.nuclei:9 | 1 380 10 | -1116 376 4 | -107 3 0 |
## 60 | Bare.nuclei:10 | 21 934 21 | -1081 934 53 | -19 0 0 |
## 61 | Bl.cromatin:1 | 24 946 11 | 587 940 18 | 44 5 1 |
## 62 | Bl.cromatin:2 | 26 950 11 | 568 946 18 | 39 4 1 |
## 63 | Bl.cromatin:3 | 26 663 7 | 232 615 3 | -65 48 2 |
## 64 | Bl.cromatin:4 | 6 642 11 | -864 605 10 | -215 38 6 |
## 65 | Bl.cromatin:5 | 6 555 11 | -804 521 8 | -204 34 5 |
## 66 | Bl.cromatin:6 | 1 555 9 | -890 386 2 | -588 169 10 |
## 67 | Bl.cromatin:7 | 12 851 15 | -1048 827 27 | -179 24 7 |
## 68 | Bl.cromatin:8 | 5 706 13 | -1226 648 15 | 366 58 12 |
## 69 | Bl.cromatin:9 | 2 463 11 | -1206 453 6 | 172 9 1 |
## 70 | Bl.cromatin:10 | 3 811 13 | -1268 523 11 | 940 288 56 |
## 71 | Normal.nucleoli:1 | 70 984 12 | 485 981 35 | 29 4 1 |
## 72 | Normal.nucleoli:2 | 6 107 8 | 120 51 0 | -126 56 2 |
## 73 | Normal.nucleoli:3 | 7 507 10 | -644 462 6 | -201 45 5 |
## 74 | Normal.nucleoli:4 | 3 535 10 | -820 385 4 | -512 150 15 |
## 75 | Normal.nucleoli:5 | 3 610 10 | -977 575 6 | -241 35 4 |
## 76 | Normal.nucleoli:6 | 4 559 10 | -754 456 4 | -357 103 9 |
## 77 | Normal.nucleoli:7 | 3 595 11 | -1155 593 7 | -64 2 0 |
## 78 | Normal.nucleoli:8 | 4 692 11 | -1129 673 10 | -190 19 3 |
## 79 | Normal.nucleoli:9 | 2 517 11 | -1085 489 6 | -258 28 3 |
## 80 | Normal.nucleoli:10 | 10 928 18 | -1267 793 33 | 522 135 52 |
## 81 | Mitoses:1 | 92 982 4 | 227 979 10 | -12 3 0 |
## 82 | Mitoses:2 | 6 741 10 | -796 609 8 | -372 133 15 |
## 83 | Mitoses:3 | 5 772 12 | -1144 768 15 | -74 3 1 |
## 84 | Mitoses:4 | 2 525 11 | -1268 512 7 | -206 13 2 |
## 85 | Mitoses:5 | 1 339 9 | -846 239 1 | 547 100 6 |
## 86 | Mitoses:6 | 0 292 10 | -1446 274 2 | 371 18 1 |
## 87 | Mitoses:7 | 1 528 10 | -1187 452 4 | 488 76 7 |
## 88 | Mitoses:8 | 1 306 10 | -1030 301 3 | 140 6 0 |
## 89 | Mitoses:10 | 2 751 12 | -1341 463 9 | 1058 288 50 |# Dim1 explains 65.8% of variance, of the highest dim score on scree plot. 33 dimensions explain ~88.6% of variance.
# which values I could use like PC1 in PCA?
#"rowcoord" in mjca1 will help:.
plot.mjca(mjca1)
mjca1$rowpcoord ## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.60670236 0.093148317 -0.0194645763 -0.0339920478 -0.0679413532
## [2,] -0.67713460 -0.568312780 -0.5710272022 -0.9223240981 0.7957212383
## [3,] 0.58140352 0.035735465 -0.0517082388 -0.0219969529 0.1303154817
## [4,] -0.63869859 -0.261121408 1.0222161072 0.8210721236 1.3059904813
## [5,] 0.54587161 -0.002697945 0.0940041356 0.0067468532 0.0260952186
## [6,] -1.49085120 1.076066095 0.5478778388 -1.0914567387 0.7082658028
## [7,] 0.44934524 0.096811484 0.0192649136 -0.1025567916 -0.1379838327
## [8,] 0.64547145 0.007046507 -0.0647849879 0.0095033584 0.0166632459
## [9,] 0.58228667 0.432198770 -0.0266168335 0.2753872274 -0.3994286278
## [10,] 0.67556178 0.016013325 0.0002533900 -0.0189274323 0.2017063942
## [11,] 0.72999692 0.172657736 0.1763149161 -0.0476324042 -0.1648406639
## [12,] 0.75301983 0.154444713 0.1261477196 -0.0122699770 -0.1436747828
## [13,] -0.28505505 -0.857740287 -0.5309088085 -0.4663524368 0.0648873933
## [14,] 0.58527182 -0.015448150 -0.0091486054 -0.1495432357 0.0533481457
## [15,] -1.56627214 -0.341420199 0.0647221833 -2.4527460932 0.3527272050
## [16,] -0.86202769 -1.085312369 -0.8735996198 0.2212106150 -0.0626975817
## [17,] 0.72650889 0.132198496 0.1323574802 -0.0148536952 0.0136752641
## [18,] 0.67199796 0.081089342 0.0932921609 -0.0212693150 0.0135736037
## [19,] -1.19663578 -0.862123854 0.7394190742 -0.2515589968 -0.3817647153
## [20,] 0.52280977 0.133962448 0.1413363176 0.1033050009 -0.1662691630
## [21,] -1.15281251 -0.874777363 -0.2946183542 -1.8235180282 -0.1501872060
## [22,] -1.19800413 -0.540289385 -0.1907416530 1.5137672750 -1.1333385536
## [23,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [24,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [25,] -0.21214729 -1.018734728 -0.7905925237 1.0354170147 -0.1846379621
## [26,] 0.69848019 0.045417052 0.0456237493 -0.0481393738 0.0510139009
## [27,] 0.66121329 0.144257471 0.0196007430 -0.0275764280 -0.0678396928
## [28,] 0.75301983 0.154444713 0.1261477196 -0.0122699770 -0.1436747828
## [29,] 0.65699386 0.034216507 -0.0384227072 0.0575957224 -0.0775981423
## [30,] 0.74942729 0.161602224 0.1777278395 -0.0440656366 -0.1370172292
## [31,] 0.69850890 0.103335559 0.0870824003 -0.0186855968 -0.1437764432
## [32,] -1.34753758 -0.579352655 0.8645505009 -0.6451538713 -0.4917263196
## [33,] 0.60246771 0.003614281 -0.0268722617 0.0485829372 -0.0775245307
## [34,] 0.67994736 0.024335348 -0.0524678713 -0.0031000227 0.0947716833
## [35,] 0.75301983 0.154444713 0.1261477196 -0.0122699770 -0.1436747828
## [36,] -1.19928144 1.115978958 0.6032818339 0.6364387608 -0.5754629039
## [37,] 0.28103339 0.002771525 0.2726454433 0.2024663528 -0.2180207989
## [38,] -0.67409211 -0.707209574 -1.4865931427 -0.5081146686 0.4388594933
## [39,] -0.76269814 -0.827584223 -0.2580280635 1.4050156830 -0.9225944680
## [40,] -0.76557290 -1.235835840 -1.2510904382 0.5102855643 0.0440764264
## [41,] -1.32504105 0.685068295 -0.7094217557 0.2082749015 -0.5824656176
## [42,] -0.40149342 -0.176970919 -0.3179798727 -0.0705243658 -0.5703815060
## [43,] -1.16547582 1.174128949 -0.0923094513 0.4893341863 -0.3444874362
## [44,] 0.60235398 0.005591087 0.1348065281 0.0695779322 -0.0142783810
## [45,] -1.04752498 -0.997038475 1.4455975265 -0.6010148998 -0.0554086676
## [46,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [47,] 0.54587161 -0.002697945 0.0940041356 0.0067468532 0.0260952186
## [48,] -1.12752916 -1.204350531 1.5537117701 0.4495315019 -0.5236469425
## [49,] -0.36319281 0.212563584 0.1729042305 0.3448770976 -0.1538549215
## [50,] -0.24471053 -0.856786151 -0.3034999739 0.1074755982 0.2764548558
## [51,] -1.01206567 -0.737747325 -0.7981037304 0.3565007136 0.4728350881
## [52,] -1.33324364 0.020728134 0.1762860867 0.4063980836 -2.2298344975
## [53,] -1.02599515 -0.519759506 0.2506751218 0.6180498527 -2.0732728476
## [54,] -0.82123463 -0.851552591 -0.3784235893 -0.0468259591 -0.0551705706
## [55,] -0.79029253 0.482674176 0.1109482852 -0.1376791174 0.6619527097
## [56,] -0.67004320 -0.762801798 0.1385277442 -1.9745951640 0.4240294871
## [57,] -0.25296295 -0.176351981 -0.5203539717 -0.2187545130 0.2572517065
## [58,] -0.44256403 -0.411167295 -0.5021657637 -0.0610794102 -0.4662254691
## [59,] -0.77680060 -0.750391702 -0.6605519111 -0.1775091453 0.3068448174
## [60,] 0.67099501 0.149009286 0.0250094765 -0.0127324809 0.1026953678
## [61,] -0.87983618 1.098364586 -0.2751003774 0.1866747350 -0.4040600962
## [62,] -0.40581164 -0.568284850 0.0808015429 -0.2743998273 0.2207498092
## [63,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [64,] -0.70355971 -0.160073616 -1.4170131630 0.6655927114 0.5468603573
## [65,] 0.67199796 0.081089342 0.0932921609 -0.0212693150 0.0135736037
## [66,] -0.68566395 -0.444697860 -0.4810078119 -0.3316187644 -0.0874634322
## [67,] -1.29453228 -0.340163492 1.4346941192 0.9383469477 1.1221912107
## [68,] 0.65450148 0.055225029 0.0410473068 -0.0127738896 0.1611627721
## [69,] 0.54708006 -0.006963189 -0.1749883004 0.0498606006 -0.0268181069
## [70,] -1.20212192 1.144613980 0.2211526053 0.5420069758 -0.2860398916
## [71,] 0.10265166 -0.480123306 -0.3286226169 0.2617462748 0.2092719569
## [72,] -1.27778284 -0.170162675 -0.5955382823 -0.2766519897 -0.5822593158
## [73,] -0.63658860 -0.647363024 -0.5944146654 0.1808972368 0.9917033184
## [74,] 0.32683678 -0.148960588 -0.3390629661 -0.0608180148 0.5100056142
## [75,] 0.57102394 -0.024695171 -0.0767455712 -0.2133031026 0.1715806759
## [76,] 0.43076845 -0.183886628 -0.3405650306 0.0534949600 0.1076814488
## [77,] 0.55019126 -0.077612817 -0.0468010014 -0.1523920879 0.0810699200
## [78,] 0.59492291 -0.049647252 0.0015364367 0.1525654832 -0.0476284988
## [79,] 0.40369507 -0.124144416 0.0665241378 0.1086647104 -0.0350883900
## [80,] 0.63046769 0.032477219 0.0184028182 0.0524148387 0.0799271765
## [81,] 0.55575525 -0.023036855 -0.1515686666 -0.0380657849 0.1200897770
## [82,] 0.37413177 -0.020248110 0.1333766546 0.0940147949 -0.0381180610
## [83,] -1.41383767 0.219464348 1.2055538674 0.0316442639 -1.7813081135
## [84,] -1.11296882 1.170525472 -0.7409754850 0.6011408328 0.5517056017
## [85,] -0.80375443 -1.227764338 0.2738090008 -0.5691263388 -0.6676134828
## [86,] -1.23621740 -1.063203284 -0.0293001765 -0.5744710549 -0.8150035784
## [87,] 0.67199796 0.081089342 0.0932921609 -0.0212693150 0.0135736037
## [88,] 0.49888171 -0.149368529 -0.1124182253 0.2198340171 0.0186234137
## [89,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [90,] 0.64000533 0.023551223 0.0045592783 0.0445783756 -0.0246460415
## [91,] 0.67199796 0.081089342 0.0932921609 -0.0212693150 0.0135736037
## [92,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [93,] 0.69850890 0.103335559 0.0870824003 -0.0186855968 -0.1437764432
## [94,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [95,] 0.66004036 0.057371537 0.0313074811 0.0635973765 -0.1026528185
## [96,] 0.60670236 0.093148317 -0.0194645763 -0.0339920478 -0.0679413532
## [97,] -1.13622829 0.704319867 0.4890650625 -0.1681369702 1.2909441293
## [98,] -1.57175729 -0.900417428 0.3988480758 -0.7825604101 -1.1556725765
## [99,] -0.84919222 -0.019423162 -0.5906993655 0.2985847808 0.0667560797
## [100,] -0.21528613 -0.726340778 -0.5150282519 -0.1880270219 0.3742674736
## [101,] 0.61896050 -0.015199710 -0.0585752274 0.0069196402 0.1740132928
## [102,] -0.31833613 -0.287278253 -0.0727595791 -0.0629948297 0.3963401489
## [103,] -1.42403790 1.541920373 0.1726227407 1.0798275146 -0.0750022807
## [104,] -0.67152127 -1.083267845 -0.6629616719 -0.2687846810 0.2577535959
## [105,] -0.88794408 0.834926885 -0.2060549641 -0.0486489647 -0.5654864698
## [106,] -1.07214242 0.130488920 0.1400266930 -0.8054505696 0.5164650130
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## [167,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
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## [171,] 0.69850890 0.103335559 0.0870824003 -0.0186855968 -0.1437764432
## [172,] -1.06826940 1.038484689 -0.6618692501 -0.4110880337 -0.1441403863
## [173,] 0.67199796 0.081089342 0.0932921609 -0.0212693150 0.0135736037
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## [176,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
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## [180,] 0.71495138 0.144313382 0.1654107229 -0.0314622555 -0.2151256666
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## [183,] -1.16257017 0.136641967 0.7685587240 -0.6177482151 0.4682535635
## [184,] 0.54847410 -0.135725920 -0.2287065402 0.0385075460 0.1355612756
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## [186,] -1.63791704 0.584477858 -0.7328899455 -0.2209268241 -0.6368655083
## [187,] 0.66121329 0.144257471 0.0196007430 -0.0275764280 -0.0678396928
## [188,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [189,] 0.67847388 0.069515245 0.0603341976 -0.0377045977 -0.0657696662
## [190,] 0.67199796 0.081089342 0.0932921609 -0.0212693150 0.0135736037
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## [193,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
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## [196,] -1.10254293 0.218515995 0.8475084990 0.7916476705 0.5502519964
## [197,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [198,] 0.60670236 0.093148317 -0.0194645763 -0.0339920478 -0.0679413532
## [199,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [200,] -1.42377151 1.330271557 -0.7011392146 0.3370662535 -0.1315501244
## [201,] -0.97019699 0.305937718 0.0261459181 -0.5757751885 0.6468017547
## [202,] 0.72999692 0.172657736 0.1763149161 -0.0476324042 -0.1648406639
## [203,] 0.72999692 0.172657736 0.1763149161 -0.0476324042 -0.1648406639
## [204,] 0.62314484 0.134126141 0.0588637463 -0.0467687065 -0.1392905765
## [205,] -1.74725030 1.536876252 0.2603129238 -0.8631400941 -0.0425120344
## [206,] -1.37201556 0.156550942 1.5738278100 0.0287265734 0.0366334067
## [207,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [208,] -1.73163511 1.219030971 -0.3083551255 -1.1885924878 -0.2861099324
## [209,] -1.31499371 1.108529105 -1.1472216492 -0.0483910772 -0.4372135860
## [210,] -1.46834047 -0.070018830 1.0760321266 -0.4506329936 1.7663766771
## [211,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [212,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [213,] -1.49192121 0.716184328 0.9709113158 1.9120595144 0.7459731182
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## [216,] -1.19824157 0.256996806 -0.2154476215 -0.3987919765 0.8956496818
## [217,] 0.42880968 0.048868172 0.2118347189 -0.0689694982 0.1140051131
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## [219,] -1.35290850 -1.121852024 0.0767074435 0.8532652905 -1.3658921199
## [220,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [221,] -1.32010005 -0.763430825 1.0724574773 0.8767551771 -0.9752451134
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## [223,] 0.72999692 0.172657736 0.1763149161 -0.0476324042 -0.1648406639
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## [236,] 0.69850890 0.103335559 0.0870824003 -0.0186855968 -0.1437764432
## [237,] 0.35780547 0.022745767 -0.0435746290 -0.3897988490 0.1811459504
## [238,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [239,] 0.41359080 -0.040352741 -0.2454616746 0.0489841309 0.1943957072
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## [249,] 0.73604653 0.123272501 0.1185139403 -0.0226901584 -0.0908979540
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## [262,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
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## [269,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [270,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [271,] -1.02986802 -1.058085098 0.0178107577 2.3763798106 -0.5488346899
## [272,] 0.67847388 0.069515245 0.0603341976 -0.0377045977 -0.0657696662
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## [277,] -1.70590494 1.551463154 -0.5211069014 -0.7798516987 0.0166920239
## [278,] -1.70219206 2.023769198 -1.0004769764 0.1118961945 -0.0142418722
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## [282,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [283,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
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## [289,] -1.24852910 -0.023602970 0.0922968495 0.1053033835 0.6618042068
## [290,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [291,] -1.79945517 1.997103379 -0.3521973647 3.0705118609 0.9303619455
## [292,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [293,] -0.72011435 -0.733954313 -1.2553636361 -0.2618548576 0.9536002784
## [294,] -1.27117142 -0.553462144 0.3945396949 -0.5200345233 0.3840472084
## [295,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [296,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [297,] -1.44802549 -1.000621005 1.6639005630 -0.1353128278 -0.4734724824
## [298,] 0.32272492 -0.039418900 -0.0812270249 -0.3926477012 0.2088677247
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## [300,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
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## [302,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
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## [304,] -0.87899917 -0.787345660 -0.6631453757 -0.0841508934 -0.9499961518
## [305,] -1.32368507 -0.039118646 2.2661660671 0.9703851587 -0.9645588994
## [306,] 0.46771595 0.040396132 0.3205032423 -0.3443423037 -0.1943866996
## [307,] -0.80087563 -0.777763833 -0.5607522839 0.1681872222 0.3447760889
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## [309,] 0.67847388 0.069515245 0.0603341976 -0.0377045977 -0.0657696662
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## [362,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
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## [371,] 0.75608155 0.157092814 0.1452621431 -0.0036711575 -0.1689047310
## [372,] 0.01331538 -0.612192931 -0.7029604405 0.2032741728 0.6220542028
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## [377,] 0.67202417 0.083067789 0.0230972509 0.0388284083 -0.0271378676
## [378,] -1.21939414 -0.945144058 1.1344208270 0.7763552097 -0.3101695430
## [379,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [380,] 0.78756957 0.226414991 0.2344946589 -0.0326179649 -0.1899689516
## [381,] 0.60298503 -0.084616765 -0.1896412208 0.0449231658 0.1356629360
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## [383,] 0.67847388 0.069515245 0.0603341976 -0.0377045977 -0.0657696662
## [384,] 0.72957061 0.134846597 0.1514719036 -0.0062548757 -0.0115546841
## [385,] 0.62298475 -0.072015655 -0.0896438601 -0.0132808592 0.3770173369
## [386,] 0.60604675 -0.081968665 -0.1705267974 0.0535219853 0.1104329878
## [387,] -1.35365851 0.636868646 0.9184497513 1.5288974949 2.0214450613
## [388,] 0.73604653 0.123272501 0.1185139403 -0.0226901584 -0.0908979540
## [389,] 0.41267642 -0.235386011 -0.4211994120 0.0636634546 0.0824511223
## [390,] 0.55661313 0.090802221 0.0976159661 0.3155715823 0.2772647077
## [391,] 0.53500068 -0.090990174 -0.0321650659 0.0261829807 0.3365872293
## [392,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [393,] 0.62252433 -0.080275727 -0.1516139983 0.0092615229 0.3621460833
## [394,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [395,] 0.31795625 -0.354877374 -0.5369931979 0.1062823912 0.3882695354
## [396,] 0.67994736 0.024335348 -0.0524678713 -0.0031000227 0.0947716833
## [397,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [398,] -1.31181051 0.891171025 -0.2990479766 0.8519844555 -0.3935587168
## [399,] 0.55366490 -0.003140735 -0.1713319646 -0.0058030926 0.0924983359
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## [401,] -0.25809225 -0.885775468 -0.7240156726 0.1280011012 0.1280722589
## [402,] -1.17764211 -0.082228926 0.9129718754 -0.6636279457 1.1773798392
## [403,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [404,] 0.08484190 -0.506479827 -0.5886178246 0.1931992627 0.8766321382
## [405,] 0.37583943 -0.162613789 0.1215676802 -0.2993548616 -0.1605307610
## [406,] 0.32008036 -0.373874327 -0.3300605051 -0.1002607016 0.4420623542
## [407,] -1.30088733 1.372171565 -0.0489544370 1.3158045784 0.6375201452
## [408,] 0.24058792 -0.411675408 -0.6839236080 0.1711087396 0.2019396398
## [409,] 0.54708006 -0.006963189 -0.1749883004 0.0498606006 -0.0268181069
## [410,] 0.73604653 0.123272501 0.1185139403 -0.0226901584 -0.0908979540
## [411,] -1.51794427 2.218239341 -0.7157745933 -0.4335077390 -0.1207940066
## [412,] 0.27936865 -0.343487436 -0.3847900220 0.0379316382 -0.0123296727
## [413,] -0.99766712 -0.181922597 0.5534193317 -0.8783600990 1.3159027768
## [414,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [415,] 0.75301983 0.154444713 0.1261477196 -0.0122699770 -0.1436747828
## [416,] 0.57460877 -0.122088639 -0.1660984855 0.0074445842 0.2705336616
## [417,] 0.18633544 -0.245740268 0.0582922680 0.0108748080 0.1916913457
## [418,] 0.60216033 0.067802588 -0.0373385437 -0.0054945722 0.1868145198
## [419,] 0.50593562 -0.172989010 -0.1647455634 0.0294412279 0.2700944802
## [420,] -1.05231190 -0.720032791 1.5287204100 -0.1652269364 0.1670205424
## [421,] -0.73618282 0.065222543 -0.1023723386 0.0875481712 0.2129416869
## [422,] -0.63808377 0.886932491 0.0543049456 0.2180315127 -0.3113913898
## [423,] 0.72957061 0.134846597 0.1514719036 -0.0062548757 -0.0115546841
## [424,] 0.48931103 -0.100161350 -0.0424051650 0.0991983211 0.0419885167
## [425,] 0.66427501 0.146905572 0.0387151664 -0.0189776085 -0.0930696410
## [426,] -0.91805289 0.164719795 -0.8755423152 -0.1249814251 -0.2355174933
## [427,] 0.16866912 -0.369646649 -0.2404711499 0.4003535974 0.6186478470
## [428,] 0.51671812 -0.045478182 0.0497431121 -0.1065126282 0.0407414729
## [429,] 0.67405673 0.151657387 0.0441238999 -0.0041336614 0.0774654196
## [430,] 0.27702849 -0.206443453 -0.0522479748 0.2031208085 -0.2800073789
## [431,] 0.75608155 0.157092814 0.1452621431 -0.0036711575 -0.1689047310
## [432,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [433,] 0.66427501 0.146905572 0.0387151664 -0.0189776085 -0.0930696410
## [434,] 0.78756957 0.226414991 0.2344946589 -0.0326179649 -0.1899689516
## [435,] -1.27602287 0.570342837 1.2637570678 -0.3566017421 0.3833132366
## [436,] 0.61682502 0.089389033 0.2113977776 0.0003858142 -0.0451523444
## [437,] 0.66427501 0.146905572 0.0387151664 -0.0189776085 -0.0930696410
## [438,] 0.60992018 0.039485214 0.1192259151 0.0053260098 -0.0783763391
## [439,] -1.16010101 0.230547790 0.2893170825 0.0365011270 -0.8877295488
## [440,] 0.46358099 -0.275421974 -0.2255602515 0.1749671568 0.0364107822
## [441,] 0.01739543 -0.221329150 -0.1513454291 0.1063618457 0.8575670681
## [442,] -1.29112227 -0.340867379 0.1527115198 -0.0730336167 -0.9987191895
## [443,] -1.25245816 0.495072016 0.8179654365 -0.3250261068 0.7675848768
## [444,] 0.61123755 0.050616520 -0.1131522218 0.0092113467 0.0673700482
## [445,] 0.55014178 -0.004315088 -0.1558738770 0.0584594201 -0.0520480550
## [446,] 0.53814866 0.063118285 0.0394271412 0.0090385596 -0.0805480260
## [447,] 0.54803119 0.082751640 0.1189508816 -0.0920454708 0.0682595035
## [448,] 0.45425607 0.103932416 0.2002280351 0.1463356083 -0.1788758358
## [449,] 0.67051765 0.058391714 0.0945326169 0.0158269801 0.2430995284
## [450,] 0.72957061 0.134846597 0.1514719036 -0.0062548757 -0.0115546841
## [451,] -1.59224153 0.351802134 0.9616132874 1.5173730912 1.8225360363
## [452,] -1.16525634 -0.600605559 0.2158180312 -0.2350581269 0.8442503466
## [453,] -1.31905047 -1.157772244 0.0664600342 -0.0465874178 -0.1725824396
## [454,] 0.72957061 0.134846597 0.1514719036 -0.0062548757 -0.0115546841
## [455,] 0.71502791 0.086500015 -0.0148154754 -0.0002511705 0.0670499090
## [456,] 0.74942729 0.161602224 0.1777278395 -0.0440656366 -0.1370172292
## [457,] 0.45425607 0.103932416 0.2002280351 0.1463356083 -0.1788758358
## [458,] 0.59682490 0.228697527 0.2778443829 0.1055427815 -0.2627466742
## [459,] 0.72957061 0.134846597 0.1514719036 -0.0062548757 -0.0115546841
## [460,] 0.66427501 0.146905572 0.0387151664 -0.0189776085 -0.0930696410
## [461,] 0.73604653 0.123272501 0.1185139403 -0.0226901584 -0.0908979540
## [462,] 0.67653315 0.038557545 -0.0003954846 0.0219340795 0.1488850050
## [463,] 0.72957061 0.134846597 0.1514719036 -0.0062548757 -0.0115546841
## [464,] 0.61332790 0.030720401 -0.0933889238 -0.0230513456 0.0949614892
## [465,] -1.11735159 -0.463684429 0.7695435449 0.1227149766 -0.2999192459
## [466,] 0.68071749 0.187883396 0.1170434890 -0.0317542672 -0.1644188643
## [467,] 0.26464598 -0.449414020 -0.3336801970 0.0799684479 0.1717232843
## [468,] -1.69575225 2.739676905 -0.8272758339 -0.2004486885 0.2337427796
## [469,] -1.40020774 -0.001678498 1.3243247218 -1.3580707428 1.5848233788
## [470,] 0.61123755 0.050616520 -0.1131522218 0.0092113467 0.0673700482
## [471,] 0.53316060 -0.004500358 0.1280714347 -0.1192892869 -0.0306077505
## [472,] 0.74942729 0.161602224 0.1777278395 -0.0440656366 -0.1370172292
## [473,] -1.38613398 1.596450313 -0.4505409835 0.6133585756 -0.5143638320
## [474,] -0.55972919 -0.756988040 -0.4783028450 -0.9325333220 0.2780026644
## [475,] -0.17971854 -0.501428457 -0.5184518878 0.5564532859 0.5599667061
## [476,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [477,] -0.78893743 -0.605441964 0.8112408757 0.2604256606 0.5037478288
## [478,] 0.74295137 0.173176320 0.2106858028 -0.0276303539 -0.0576739593
## [479,] -1.39549869 0.529147993 -0.9929006123 -0.0116321530 -0.3955413593
## [480,] -0.09577093 0.029149338 -0.2162964630 -0.2613516229 0.1635057194
## [481,] 0.74942729 0.161602224 0.1777278395 -0.0440656366 -0.1370172292
## [482,] 0.78756957 0.226414991 0.2344946589 -0.0326179649 -0.1899689516
## [483,] 0.67862350 0.018661425 0.0193678134 -0.0103286128 0.1764764460
## [484,] 0.72650889 0.132198496 0.1323574802 -0.0148536952 0.0136752641
## [485,] 0.72650889 0.132198496 0.1323574802 -0.0148536952 0.0136752641
## [486,] 0.52280977 0.133962448 0.1413363176 0.1033050009 -0.1662691630
## [487,] 0.72650889 0.132198496 0.1323574802 -0.0148536952 0.0136752641
## [488,] 0.63046769 0.032477219 0.0184028182 0.0524148387 0.0799271765
## [489,] 0.67199796 0.081089342 0.0932921609 -0.0212693150 0.0135736037
## [490,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [491,] 0.60164289 -0.105150322 -0.1276971713 -0.0088873043 0.0183712751
## [492,] -1.58731462 1.162674831 -0.2154624497 -1.3529645693 -0.3839087979
## [493,] 0.59169369 0.152966887 0.1352683620 0.3184204346 0.2495429334
## [494,] 0.66427501 0.146905572 0.0387151664 -0.0189776085 -0.0930696410
## [495,] 0.75608155 0.157092814 0.1452621431 -0.0036711575 -0.1689047310
## [496,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [497,] 0.66121329 0.144257471 0.0196007430 -0.0275764280 -0.0678396928
## [498,] 0.66427501 0.146905572 0.0387151664 -0.0189776085 -0.0930696410
## [499,] 0.74942729 0.161602224 0.1777278395 -0.0440656366 -0.1370172292
## [500,] -1.41522573 -0.057887219 0.4139073753 0.3364906886 -0.1487811201
## [501,] -1.06432881 0.458907235 -0.0190559080 0.5492044271 1.5259631952
## [502,] 0.78756957 0.226414991 0.2344946589 -0.0326179649 -0.1899689516
## [503,] 0.78450785 0.223766890 0.2153802354 -0.0412167844 -0.1647390035
## [504,] 0.58696788 -0.072737828 -0.1473081099 0.0727673308 0.1357936476
## [505,] -0.74931345 -0.225645331 1.0177813989 -0.6542541292 1.1869811774
## [506,] 0.61303016 -0.018654798 0.0315550533 0.1449941540 -0.0225734442
## [507,] 0.57147369 -0.069245368 0.0268606207 0.1585805845 0.0844915999
## [508,] -0.97521856 -1.092724815 -0.8645220381 0.6269759169 -0.2903093971
## [509,] -1.20800538 -0.876780056 -0.7646536561 -0.2531501782 -0.6197770618
## [510,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [511,] 0.64000533 0.023551223 0.0045592783 0.0445783756 -0.0246460415
## [512,] 0.72957061 0.134846597 0.1514719036 -0.0062548757 -0.0115546841
## [513,] 0.67199796 0.081089342 0.0932921609 -0.0212693150 0.0135736037
## [514,] 0.37020799 -0.063222234 -0.1090276451 0.2630250027 -0.0841239524
## [515,] 0.74295137 0.173176320 0.2106858028 -0.0276303539 -0.0576739593
## [516,] -1.03486494 -1.369429261 -0.4147255668 -0.0618268899 -0.1631650173
## [517,] 0.62252433 -0.080275727 -0.1516139983 0.0092615229 0.3621460833
## [518,] 0.72999692 0.172657736 0.1763149161 -0.0476324042 -0.1648406639
## [519,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [520,] 0.75301983 0.154444713 0.1261477196 -0.0122699770 -0.1436747828
## [521,] 0.50338001 -0.119262026 -0.2105571119 0.1098498171 0.0137820579
## [522,] 0.60670236 0.093148317 -0.0194645763 -0.0339920478 -0.0679413532
## [523,] 0.55366490 -0.003140735 -0.1713319646 -0.0058030926 0.0924983359
## [524,] 0.72650889 0.132198496 0.1323574802 -0.0148536952 0.0136752641
## [525,] 0.57732070 0.185071602 0.1804016369 0.1097206206 -0.1661675026
## [526,] 0.56414293 0.110477691 -0.0924416933 -0.0118687833 0.1282454551
## [527,] 0.73604653 0.123272501 0.1185139403 -0.0226901584 -0.0908979540
## [528,] 0.52987137 -0.081517250 -0.2074959452 -0.0051747545 0.0161995882
## [529,] 0.72650889 0.132198496 0.1323574802 -0.0148536952 0.0136752641
## [530,] 0.54284541 -0.096497224 -0.1823959858 0.1324355856 -0.0364012844
## [531,] 0.66121329 0.144257471 0.0196007430 -0.0275764280 -0.0678396928
## [532,] -1.35872774 1.044511828 -0.1143829433 -0.0362451394 -0.4387614677
## [533,] 0.77252403 0.198070638 0.2235904657 -0.0164478162 -0.2402539543
## [534,] 0.75248901 0.164250324 0.1968422629 -0.0354668171 -0.1622471774
## [535,] -1.30319113 -0.910932025 1.0767917398 1.0737351889 0.6264287205
## [536,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [537,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [538,] 0.24183829 -0.393251923 -0.5107316779 -0.0161797149 0.5959252832
## [539,] 0.09690290 -0.453132159 -0.3828782515 0.1164055846 0.4295798937
## [540,] 0.73604653 0.123272501 0.1185139403 -0.0226901584 -0.0908979540
## [541,] 0.09863505 -0.329335228 0.0065011184 -0.1340215337 -0.0425862970
## [542,] 0.47763001 -0.126960206 -0.2999970748 0.0510306653 0.2755338156
## [543,] 0.53814866 0.063118285 0.0394271412 0.0090385596 -0.0805480260
## [544,] 0.75301983 0.154444713 0.1261477196 -0.0122699770 -0.1436747828
## [545,] 0.66121329 0.144257471 0.0196007430 -0.0275764280 -0.0678396928
## [546,] 0.60670236 0.093148317 -0.0194645763 -0.0339920478 -0.0679413532
## [547,] 0.60670236 0.093148317 -0.0194645763 -0.0339920478 -0.0679413532
## [548,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [549,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [550,] 0.61294501 0.004634459 0.0363528741 0.0008125408 0.2682278162
## [551,] -1.30318511 1.158621350 -0.0425679640 -1.2936198796 -0.0843310237
## [552,] 0.62543643 -0.026773807 -0.0915331907 -0.0095156425 0.0946700229
## [553,] 0.59822627 -0.014929566 0.0252222813 -0.1295411854 0.1605148503
## [554,] -0.84965193 -0.589274890 -0.6485627228 -0.2037010018 0.4952297034
## [555,] -1.29601560 1.105467244 -0.4734902809 0.0379092145 0.4213638433
## [556,] -1.08967838 0.208165010 -0.1379546266 -0.0794267470 0.3600307834
## [557,] -1.48582890 -0.262967586 0.0558661462 -0.4336883042 0.9375485079
## [558,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [559,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [560,] -1.07585170 -0.609972119 1.2780714420 0.4298004140 0.6080073138
## [561,] 0.55366490 -0.003140735 -0.1713319646 -0.0058030926 0.0924983359
## [562,] 0.66121329 0.144257471 0.0196007430 -0.0275764280 -0.0678396928
## [563,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [564,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [565,] 0.71355444 0.131679912 0.0979865935 -0.0348557455 -0.0934914405
## [566,] 0.60817583 0.047968420 -0.1322666452 0.0006125272 0.0925999963
## [567,] -1.16594632 -0.114677648 0.3333591313 -0.7538292292 -0.5374018696
## [568,] -1.24456412 -0.170966093 -0.2072553915 0.0167310646 -0.4192485164
## [569,] 0.73604653 0.123272501 0.1185139403 -0.0226901584 -0.0908979540
## [570,] 0.28009021 -0.203795353 -0.0331335514 0.2117196280 -0.3052373271
## [571,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [572,] -1.49963552 1.823290452 -0.5313531516 -0.5430715562 0.0355617296
## [573,] 0.60216033 0.067802588 -0.0373385437 -0.0054945722 0.1868145198
## [574,] -0.91784546 -0.002726444 0.2653396544 -0.0369260910 1.1450676945
## [575,] 0.66427501 0.146905572 0.0387151664 -0.0189776085 -0.0930696410
## [576,] -0.64250575 0.563576589 0.4622704353 -0.2188939027 0.6400683453
## [577,] -0.99475796 -0.957769313 0.5414847467 0.4600071509 -1.5716185706
## [578,] -0.74504562 -0.834308506 -0.6262760768 -0.1795161806 0.5640884635
## [579,] 0.61123755 0.050616520 -0.1131522218 0.0092113467 0.0673700482
## [580,] -0.68993874 -0.648042138 0.5800017401 0.2557241648 -0.0079408157
## [581,] 0.66121329 0.144257471 0.0196007430 -0.0275764280 -0.0678396928
## [582,] 0.67347143 0.035909444 -0.0195099080 0.0133352600 0.1741149532
## [583,] 0.49256913 -0.058072343 -0.2140536198 0.0434449808 -0.0269197672
## [584,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [585,] 0.43272895 -0.135786013 -0.2288580853 -0.2206909813 0.2885827218
## [586,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [587,] 0.78450785 0.223766890 0.2153802354 -0.0412167844 -0.1647390035
## [588,] 0.72650889 0.132198496 0.1323574802 -0.0148536952 0.0136752641
## [589,] -0.89930770 -0.062507159 0.1559612459 0.3735882119 -0.3227269739
## [590,] -0.77031944 -0.221366407 0.2986696245 0.0319045272 -0.2038150742
## [591,] -1.45405816 -0.212366303 0.7376378575 0.1501751809 -1.4673315721
## [592,] 0.63352941 0.035125320 0.0375172416 0.0610136583 0.0546972284
## [593,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [594,] -1.06504937 1.810521620 -0.8276062385 -0.3506923550 -0.2814022548
## [595,] 0.66427501 0.146905572 0.0387151664 -0.0189776085 -0.0930696410
## [596,] -0.97108937 -0.588779176 -0.8187495446 0.4141734664 -0.1644461980
## [597,] -1.10027056 0.984802442 -0.3390854949 -0.1517709701 -0.1436036927
## [598,] -1.75363735 2.350380449 -0.7220130134 -0.3083582394 0.1864486662
## [599,] 0.61861619 -0.073978109 -0.1200633920 0.0015328771 -0.0344055537
## [600,] 0.76946231 0.195422537 0.2044760422 -0.0250466357 -0.2150240062
## [601,] 0.61237566 -0.019022164 -0.0622315632 0.0625833334 0.0546968500
## [602,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [603,] 0.72650889 0.132198496 0.1323574802 -0.0148536952 0.0136752641
## [604,] 0.66121329 0.144257471 0.0196007430 -0.0275764280 -0.0678396928
## [605,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [606,] -0.28878877 -0.825022624 -0.7654115249 0.4671326337 0.0672620896
## [607,] 0.32192410 -0.323328081 -0.0664263935 0.0050026120 0.0710685240
## [608,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [609,] 0.58161457 0.085514018 -0.0160255963 0.0269154472 -0.0729370037
## [610,] 0.28438298 -0.264510405 -0.2215843603 0.5578440711 0.4143325776
## [611,] -1.28933189 -0.577327908 0.4922793474 -1.0868195255 1.2018680081
## [612,] 0.56806621 0.116571953 0.1456990843 -0.0730264699 -0.0097472735
## [613,] 0.75608155 0.157092814 0.1452621431 -0.0036711575 -0.1689047310
## [614,] 0.72957061 0.134846597 0.1514719036 -0.0062548757 -0.0115546841
## [615,] 0.41530208 -0.079686129 -0.1271770734 0.1916827316 0.0376552653
## [616,] 0.66121329 0.144257471 0.0196007430 -0.0275764280 -0.0678396928
## [617,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [618,] -1.07296067 -0.588373745 0.2551597686 -1.5851879835 0.9165853411
## [619,] 0.73604653 0.123272501 0.1185139403 -0.0226901584 -0.0908979540
## [620,] 0.53900510 -0.084211737 -0.0952835438 -0.2075531353 0.1740725020
## [621,] -1.45704232 1.160674650 0.3116212666 -0.5590021978 -0.4711290274
## [622,] 0.25532365 -0.309037980 -0.3248745557 -0.1600665963 0.6752836130
## [623,] 0.72957061 0.134846597 0.1514719036 -0.0062548757 -0.0115546841
## [624,] 0.53814866 0.063118285 0.0394271412 0.0090385596 -0.0805480260
## [625,] 0.60344426 0.051059310 0.1521838784 0.0217612925 0.0009669308
## [626,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [627,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [628,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [629,] 0.75608155 0.157092814 0.1452621431 -0.0036711575 -0.1689047310
## [630,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [631,] 0.66714253 -0.027037056 -0.1278051422 0.0042739119 0.2298510910
## [632,] 0.64500074 0.101649881 0.1568783110 0.0081748620 -0.1060981133
## [633,] -1.43556865 2.581436814 -1.0459543305 -0.0403472033 0.2134592937
## [634,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [635,] 0.30247501 -0.213011022 -0.1409499789 0.5476755764 0.4395629042
## [636,] 0.59099191 -0.017183392 0.0056597974 -0.0044976946 0.1071629650
## [637,] 0.60216033 0.067802588 -0.0373385437 -0.0054945722 0.1868145198
## [638,] 0.72650889 0.132198496 0.1323574802 -0.0148536952 0.0136752641
## [639,] 0.67847388 0.069515245 0.0603341976 -0.0377045977 -0.0657696662
## [640,] 0.73298481 0.120624400 0.0993995169 -0.0312889779 -0.0656680058
## [641,] 0.66121329 0.144257471 0.0196007430 -0.0275764280 -0.0678396928
## [642,] -0.32741515 -0.461737955 -0.9921051741 0.0766416911 -0.8055260704
## [643,] -1.32195695 -0.600267032 0.7929612616 1.1334839682 1.2954497694
## [644,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [645,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [646,] 0.67199796 0.081089342 0.0932921609 -0.0212693150 0.0135736037
## [647,] 0.65393214 0.031568406 -0.0575371306 0.0489969029 -0.0523681942
## [648,] 0.65393214 0.031568406 -0.0575371306 0.0489969029 -0.0523681942
## [649,] 0.60685846 0.036837113 0.1001114917 -0.0032728097 -0.0531463909
## [650,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [651,] 0.29853786 -0.342487908 -0.3614563588 0.1704242014 0.4007644899
## [652,] 0.67847388 0.069515245 0.0603341976 -0.0377045977 -0.0657696662
## [653,] -0.84916928 0.015873688 0.2108863176 -0.5925654794 0.4114172229
## [654,] -1.20617622 0.986450749 0.4067298290 -0.3321485285 -0.4838406980
## [655,] -1.10168950 -0.219188219 1.5804671536 -0.3594678171 -1.4651852374
## [656,] 0.53148558 -0.146391204 -0.1857245547 0.0254901991 0.1885133764
## [657,] 0.69850890 0.103335559 0.0870824003 -0.0186855968 -0.1437764432
## [658,] 0.31873699 -0.381898267 -0.4839746164 0.1878496609 0.2726855613
## [659,] 0.76806537 0.182789067 0.1370519128 -0.0284401257 -0.0933897801
## [660,] 0.53252918 -0.072637641 -0.0623255805 -0.1911178526 0.2534157719
## [661,] 0.71502791 0.086500015 -0.0148154754 -0.0002511705 0.0670499090
## [662,] 0.66427501 0.146905572 0.0387151664 -0.0189776085 -0.0930696410
## [663,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [664,] 0.75608155 0.157092814 0.1452621431 -0.0036711575 -0.1689047310
## [665,] -1.71488662 1.900608197 -0.4940907391 -0.7456239270 -0.8655176678
## [666,] -1.37427740 0.527794389 -1.0217746665 -0.5917347233 -0.3059825524
## [667,] 0.54764941 0.016693434 -0.0764038630 -0.0119101920 0.1867128594
## [668,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [669,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [670,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [671,] 0.77112709 0.185437167 0.1561663363 -0.0198413062 -0.1186197283
## [672,] 0.55011164 0.007503133 -0.2370160969 0.0698491940 -0.0275927848
## [673,] 0.72957061 0.134846597 0.1514719036 -0.0062548757 -0.0115546841
## [674,] 0.56745322 0.260158347 0.3948045928 0.7068503855 0.1853696415
## [675,] 0.64500074 0.101649881 0.1568783110 0.0081748620 -0.1060981133
## [676,] -1.07143730 0.079732053 0.0444095883 -0.6851746814 0.0823018905
## [677,] 0.73604653 0.123272501 0.1185139403 -0.0226901584 -0.0908979540
## [678,] 0.56727342 -0.056573580 0.0971541321 0.0667290800 0.0134433933
## [679,] 0.48087925 -0.114599245 -0.1181397790 0.1578529465 0.2012334779
## [680,] 0.75608155 0.157092814 0.1452621431 -0.0036711575 -0.1689047310
## [681,] -1.22877226 0.996442365 -0.1443238579 -0.2548140578 0.3154939290
## [682,] -0.85025572 -0.498306146 -0.1994170231 0.6354649292 0.4301394311
## [683,] -1.01936871 -0.213082090 1.1645502330 -0.5083030515 0.8548911073
## [,6] [,7] [,8] [,9]
## [1,] 2.470197e-02 0.0338488586 -7.115866e-02 0.0180861256
## [2,] 2.000261e-02 -0.1409691955 -6.614998e-01 -0.5752074932
## [3,] -2.878616e-01 0.1858920371 1.895521e-02 -0.0781030033
## [4,] -6.549112e-01 0.0061944224 1.430800e-01 0.0288348413
## [5,] 1.237779e-01 -0.1219398551 -9.728167e-02 0.0567525889
## [6,] 4.072717e-01 -0.3703207689 -1.457888e+00 -0.0269852311
## [7,] 2.323455e-01 -0.1097152709 -3.946887e-02 0.0565798352
## [8,] -1.845269e-01 0.0503276333 -9.787578e-02 -0.0301681354
## [9,] 5.130038e-01 -0.3504298612 7.593698e-01 -0.0072666810
## [10,] -1.224262e-01 -0.0256954022 4.651640e-02 0.1034273163
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## [12,] 1.856443e-01 -0.1392131632 2.410362e-02 -0.1092138133
## [13,] -6.766145e-01 0.5389941113 4.684409e-01 0.3325237446
## [14,] 4.458885e-02 0.0536590741 1.716028e-01 -0.1758673272
## [15,] 1.774845e+00 1.0181771036 -7.404410e-01 -2.0965494893
## [16,] 3.099177e-01 -0.4016118597 5.791753e-01 -0.3136263891
## [17,] 1.386883e-01 -0.1976560553 4.792934e-02 -0.0588683739
## [18,] 1.012646e-01 -0.1068812555 -4.445051e-02 -0.0433590013
## [19,] 2.367992e-01 -0.5642416917 -8.975761e-02 -0.6013836102
## [20,] -1.752168e-01 0.1420943971 -2.430758e-01 0.1190331678
## [21,] 4.099368e-01 0.6766196056 4.924683e-01 1.1794316400
## [22,] 5.281670e-01 0.0031454467 5.224265e-01 -0.3589826188
## [23,] 7.292228e-02 -0.0052112694 1.574403e-02 -0.0733415328
## [24,] 1.523420e-01 -0.0340544029 -3.639761e-02 -0.0170166633
## [25,] 2.404118e-01 0.2988427866 -2.344282e-01 0.0068187215
## [26,] -1.235778e-01 0.1400668421 1.868117e-02 0.0874138522
## [27,] 6.212564e-02 -0.0569259412 2.122119e-02 0.0025767529
## [28,] 1.856443e-01 -0.1392131632 2.410362e-02 -0.1092138133
## [29,] 1.595789e-01 -0.0297710716 9.005009e-02 0.1894571078
## [30,] 1.375367e-01 -0.0318938111 2.009410e-02 -0.0748818381
## [31,] 1.482207e-01 -0.0484383634 -6.827622e-02 -0.0937044407
## [32,] 1.085231e-01 0.9296197777 1.341422e-01 0.6171986252
## [33,] -1.011395e-01 -0.0316873733 -7.742605e-02 0.0076099187
## [34,] -2.598253e-01 0.0935547273 -1.385553e-02 -0.0098052276
## [35,] 1.856443e-01 -0.1392131632 2.410362e-02 -0.1092138133
## [36,] -3.922253e-01 0.1131144846 -1.017815e+00 -0.4284117196
## [37,] -3.549556e-01 0.2213164887 -4.713437e-02 0.4102515858
## [38,] 8.955963e-01 -0.0487788315 1.039544e+00 -0.3490868539
## [39,] 9.266947e-01 0.1510109748 3.944102e-01 -0.1208409381
## [40,] 2.920435e-01 -0.4220240984 -7.399867e-01 -0.4082993451
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## [558,] 7.292228e-02 -0.0052112694 1.574403e-02 -0.0733415328
## [559,] 1.897657e-01 -0.1248292027 5.598223e-02 -0.0325260360
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## [571,] 2.056432e-01 -0.1011519093 2.753441e-02 0.0003709560
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## [579,] -2.547444e-01 0.0655173488 -3.682619e-02 0.0990100502
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## [586,] 7.292228e-02 -0.0052112694 1.574403e-02 -0.0733415328
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## [608,] 2.056432e-01 -0.1011519093 2.753441e-02 0.0003709560
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## [628,] 2.056432e-01 -0.1011519093 2.753441e-02 0.0003709560
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## [630,] 7.292228e-02 -0.0052112694 1.574403e-02 -0.0733415328
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## [643,] 5.348254e-01 0.5080443414 8.499206e-01 1.0942907442
## [644,] 2.056432e-01 -0.1011519093 2.753441e-02 0.0003709560
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## [668,] 2.056432e-01 -0.1011519093 2.753441e-02 0.0003709560
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## [679,] -3.727639e-01 0.1349177629 -2.461952e-02 -0.0922809963
## [680,] 2.015219e-01 -0.1155358698 -4.344195e-03 -0.0763168213
## [681,] -1.049028e-01 0.0388431973 -1.056584e+00 -0.4600302013
## [682,] -2.810270e-01 -0.7339208773 -7.165207e-02 -0.3103001085
## [683,] -1.710879e-01 -0.6988562830 1.203811e+00 -0.1913936636
## [,10] [,11] [,12] [,13]
## [1,] 0.081313250 -0.0491149789 0.0698191540 -0.0434645550
## [2,] -0.013585072 0.3604850878 0.6350158794 -0.6041697264
## [3,] -0.001202664 0.1678785340 -0.0049387548 0.1986346895
## [4,] -0.752041025 -1.6780059840 -0.5186168204 0.0020604523
## [5,] -0.256693193 0.1221129915 0.0798966032 -0.2121968839
## [6,] -1.132133147 0.4671433783 0.2551311233 -0.5515074425
## [7,] -0.038651998 -0.0652520405 -0.1018106065 0.0123542214
## [8,] 0.194657571 0.0443664888 -0.1144553556 0.0355697288
## [9,] 0.456566280 -0.1053210567 -0.8353562985 -0.6836118978
## [10,] 0.141146530 0.0912547737 -0.0050672392 0.0810184972
## [11,] -0.144232062 0.0456836073 -0.0596699756 -0.0655780035
## [12,] 0.024645234 0.0538077760 -0.0649080294 -0.0551621917
## [13,] 0.478994483 0.1417004910 0.4821832081 -0.5002567575
## [14,] 0.098570142 0.0644263450 -0.2478161029 -0.3093325937
## [15,] 0.075333881 1.0925032792 -0.3214883403 -0.3177334569
## [16,] 0.299385433 0.8175363109 0.6812337157 0.8251760079
## [17,] -0.066204209 0.0007120358 0.0199733564 0.0193135164
## [18,] -0.095022399 -0.0240125173 -0.0063444072 -0.0592129424
## [19,] 0.509805613 -0.8039813188 0.4664670923 0.6852912101
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## [507,] -0.195712933 -0.1970542508 -0.0702049739 -0.1611232651
## [508,] -0.675406527 0.0236086422 0.6703576371 -0.0346328091
## [509,] -0.279586899 0.2272449898 -0.3605475968 1.3417645800
## [510,] -0.026931145 0.1078964081 0.0068333475 0.1201497387
## [511,] -0.122767433 0.0053542819 0.0014535977 0.2274831255
## [512,] -0.104877942 -0.0700652170 0.0614921339 -0.0432008156
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## [514,] 0.058747525 -0.3729222608 -0.0878157947 -0.1608255275
## [515,] -0.143727451 0.0320864512 0.0004371236 -0.0231968191
## [516,] 0.634342356 0.5865771422 -0.7921543269 0.1080381226
## [517,] 0.339977057 0.1065380397 -0.0282968019 0.2502768765
## [518,] -0.144232062 0.0456836073 -0.0596699756 -0.0655780035
## [519,] -0.026931145 0.1078964081 0.0068333475 0.1201497387
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## [523,] 0.280143777 -0.0338317130 0.0465895913 0.1257938242
## [524,] -0.066204209 0.0007120358 0.0199733564 0.0193135164
## [525,] -0.039231601 -0.1695439268 -0.0009241472 -0.0566026778
## [526,] 0.164678111 0.0603162533 0.1106825790 0.1920733133
## [527,] -0.065604878 0.0371191553 0.0483521250 0.0576354068
## [528,] 0.145644418 -0.1933753544 0.1211852726 -0.1363360786
## [529,] -0.066204209 0.0007120358 0.0199733564 0.0193135164
## [530,] 0.161298092 -0.0787933052 -0.1933184544 -0.0968707095
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## [534,] -0.143128120 0.0684935707 0.0288158923 0.0151250713
## [535,] 0.824761302 -0.3645683676 -0.2636949741 0.6133705944
## [536,] -0.026931145 0.1078964081 0.0068333475 0.1201497387
## [537,] -0.066708821 0.0143091919 -0.0401337428 -0.0230676680
## [538,] 0.252234618 0.2486254005 0.3168221185 0.7602765740
## [539,] 0.400156854 -0.0779220649 0.5832846473 0.2674751747
## [540,] -0.065604878 0.0371191553 0.0483521250 0.0576354068
## [541,] 0.022936378 0.0279344521 0.3047075677 0.4024403146
## [542,] 0.381626909 0.0810451201 -0.0185680008 0.3933626471
## [543,] -0.090213087 0.0509578302 0.2238967055 -0.1804363697
## [544,] 0.024645234 0.0538077760 -0.0649080294 -0.0551621917
## [545,] 0.110131440 -0.0243904258 0.0961369176 0.0350619037
## [546,] 0.081313250 -0.0491149789 0.0698191540 -0.0434645550
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## [548,] -0.066708821 0.0143091919 -0.0401337428 -0.0230676680
## [549,] -0.026931145 0.1078964081 0.0068333475 0.1201497387
## [550,] -0.098967853 -0.0233203444 0.0038624100 -0.0143737047
## [551,] 0.666897654 -0.6736177219 0.7225865672 -0.1266611771
## [552,] 0.143081192 0.0984551209 -0.0427139788 0.2108816592
## [553,] 0.099074754 0.0508291889 -0.1877090036 -0.2669514094
## [554,] 0.777732396 0.5967130974 -0.3005316690 -0.7945347093
## [555,] -0.291130567 -0.7295112677 0.1613274719 0.1610038879
## [556,] 0.001894376 -0.5073153475 -0.0556478487 -0.1799364106
## [557,] -0.354102139 0.2507796156 -0.2129877306 -0.0971865200
## [558,] -0.026931145 0.1078964081 0.0068333475 0.1201497387
## [559,] -0.037890631 0.0390337450 -0.0138159792 0.0554587908
## [560,] -1.246177199 0.0637983833 0.3272768496 -0.6275784878
## [561,] 0.280143777 -0.0338317130 0.0465895913 0.1257938242
## [562,] 0.110131440 -0.0243904258 0.0961369176 0.0350619037
## [563,] -0.037890631 0.0390337450 -0.0138159792 0.0554587908
## [564,] -0.037890631 0.0390337450 -0.0138159792 0.0554587908
## [565,] -0.066708821 0.0143091919 -0.0401337428 -0.0230676680
## [566,] 0.308961967 -0.0091071598 0.0729073550 0.2043202830
## [567,] 0.629193020 -0.2671872355 -0.1113732406 -0.6487325766
## [568,] -0.294108826 -0.6900993346 0.6056972697 -0.7893213002
## [569,] -0.065604878 0.0371191553 0.0483521250 0.0576354068
## [570,] 0.076243607 -0.4991593404 -0.2479140681 -0.1537668486
## [571,] -0.076564364 -0.0317435078 0.0277027983 -0.0070555411
## [572,] 0.453085546 -0.3027488799 0.1914614892 -0.6679110700
## [573,] 0.106185986 -0.0236982529 0.1063437348 0.0799011415
## [574,] 0.876187888 0.0448004256 -0.8874138921 -0.4101893694
## [575,] 0.071457707 -0.0951676786 0.1376556952 -0.0274524282
## [576,] -0.424669334 -1.2259891048 0.4279034141 -0.2127133006
## [577,] -0.084883958 -0.7773026211 -0.3741806727 -0.2173586533
## [578,] -0.238505407 -0.1934709343 0.4072411314 -0.1919166179
## [579,] 0.270288234 -0.0798844126 0.1144261325 0.1418059511
## [580,] -0.016591879 -0.4431052046 0.1748180217 0.3330179765
## [581,] 0.110131440 -0.0243904258 0.0961369176 0.0350619037
## [582,] 0.132626318 0.0159953017 -0.0032562062 0.1885718956
## [583,] 0.275128663 -0.1499511867 -0.0116927437 -0.2550207915
## [584,] -0.026931145 0.1078964081 0.0068333475 0.1201497387
## [585,] 0.246836059 0.2102349859 -0.0507955952 -0.0605114225
## [586,] -0.026931145 0.1078964081 0.0068333475 0.1201497387
## [587,] -0.115413873 0.0704081604 -0.0333522120 0.0129484553
## [588,] -0.066204209 0.0007120358 0.0199733564 0.0193135164
## [589,] 0.670916454 -0.0359962735 1.1021231379 0.4011780713
## [590,] 1.176926027 -0.1749558148 0.3164761839 0.2236008283
## [591,] -0.646662566 0.6279550193 0.0115804964 0.1931338695
## [592,] -0.162040498 -0.1018300904 0.0145936066 0.1266469032
## [593,] -0.076564364 -0.0317435078 0.0277027983 -0.0070555411
## [594,] 0.157289206 -0.4768438528 -0.2732810413 0.1362916265
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## [597,] 0.999281788 -0.0461107582 -0.2757023496 -0.3012469945
## [598,] 0.568016269 0.0694359774 0.2792293624 -0.2340408086
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## [600,] -0.052878008 0.0851821914 -0.0844442621 -0.0976725273
## [601,] 0.127611204 -0.1001241720 -0.0615385413 -0.1922427202
## [602,] -0.026931145 0.1078964081 0.0068333475 0.1201497387
## [603,] -0.066204209 0.0007120358 0.0199733564 0.0193135164
## [604,] 0.110131440 -0.0243904258 0.0961369176 0.0350619037
## [605,] -0.026931145 0.1078964081 0.0068333475 0.1201497387
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## [608,] -0.076564364 -0.0317435078 0.0277027983 -0.0070555411
## [609,] -0.024554357 -0.0247808838 0.0297021575 0.1623992869
## [610,] -0.094173449 -0.5842516461 -0.1330112858 -0.3944173918
## [611,] -2.014973133 0.8774292705 -0.2842614195 -0.5634267115
## [612,] -0.145839699 -0.1707893867 0.2891177625 -0.1991153651
## [613,] -0.014028499 -0.0169694768 -0.0233892518 -0.1176765237
## [614,] -0.104877942 -0.0700652170 0.0614921339 -0.0432008156
## [615,] 0.323260819 -0.2506146495 -0.0659578629 -0.2689682654
## [616,] 0.110131440 -0.0243904258 0.0961369176 0.0350619037
## [617,] -0.076564364 -0.0317435078 0.0277027983 -0.0070555411
## [618,] 0.603964988 0.0623050320 0.5531299852 -0.3720672107
## [619,] -0.065604878 0.0371191553 0.0483521250 0.0576354068
## [620,] -0.020054023 0.2206046664 -0.0955223370 0.0053817672
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## [622,] 0.079573262 0.5055724727 -0.0481550295 0.0327923257
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## [625,] -0.266548736 0.0760602918 0.1477331443 -0.1961847570
## [626,] -0.026931145 0.1078964081 0.0068333475 0.1201497387
## [627,] -0.026931145 0.1078964081 0.0068333475 0.1201497387
## [628,] -0.076564364 -0.0317435078 0.0277027983 -0.0070555411
## [629,] -0.014028499 -0.0169694768 -0.0233892518 -0.1176765237
## [630,] -0.026931145 0.1078964081 0.0068333475 0.1201497387
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## [633,] 0.369679177 0.0697053691 0.1422900403 0.5767866570
## [634,] -0.026931145 0.1078964081 0.0068333475 0.1201497387
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## [644,] -0.076564364 -0.0317435078 0.0277027983 -0.0070555411
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## [650,] -0.076564364 -0.0317435078 0.0277027983 -0.0070555411
## [651,] 0.666180877 -0.0979835558 0.0536468395 0.4577301710
## [652,] -0.055749335 0.0831718550 -0.0194844162 0.0416232800
## [653,] 0.063049551 0.2156964798 0.3336357956 -0.4947347690
## [654,] 0.202219218 0.1043490141 1.0627011283 -0.4510901215
## [655,] 0.336233064 0.5878631724 0.8243433256 0.1037068561
## [656,] 0.094438849 0.1419497195 -0.0914235391 0.2731759796
## [657,] -0.004172956 0.0290832229 -0.0912257930 -0.1336886505
## [658,] 0.253639955 -0.3050811223 -0.0337413978 -0.0850001489
## [659,] -0.037890631 0.0390337450 -0.0138159792 0.0554587908
## [660,] -0.059327087 0.1134202941 -0.0823823281 -0.0954544552
## [661,] 0.160939896 0.0543170109 -0.0370455419 0.2247171700
## [662,] 0.071457707 -0.0951676786 0.1376556952 -0.0274524282
## [663,] -0.076564364 -0.0317435078 0.0277027983 -0.0070555411
## [664,] -0.014028499 -0.0169694768 -0.0233892518 -0.1176765237
## [665,] 0.117332235 -0.7016895645 0.2716584840 -0.1609000226
## [666,] -0.104220255 -1.1148788130 -0.1516786535 0.2509384189
## [667,] 0.077367796 -0.0484228060 0.0800259712 0.0013746827
## [668,] -0.076564364 -0.0317435078 0.0277027983 -0.0070555411
## [669,] -0.076564364 -0.0317435078 0.0277027983 -0.0070555411
## [670,] -0.076564364 -0.0317435078 0.0277027983 -0.0070555411
## [671,] -0.076564364 -0.0317435078 0.0277027983 -0.0070555411
## [672,] -0.305480846 0.3202648022 0.0088557878 0.3949734476
## [673,] -0.104877942 -0.0700652170 0.0614921339 -0.0432008156
## [674,] -0.597089752 0.2562081676 -0.5677921427 0.2988248151
## [675,] -0.238235158 0.1143820010 0.1139438087 -0.1600394826
## [676,] -0.030785964 -0.3706141429 1.4376873786 -0.1111169726
## [677,] -0.065604878 0.0371191553 0.0483521250 0.0576354068
## [678,] 0.218773314 0.0310194004 0.0179931774 0.2045212590
## [679,] -0.101893198 -0.0051631995 -0.0687993215 0.0967243667
## [680,] -0.014028499 -0.0169694768 -0.0233892518 -0.1176765237
## [681,] 0.747839423 0.2167064085 0.3355710551 -0.8826284897
## [682,] 0.090629136 -1.8753502109 0.2180475440 -0.1324892066
## [683,] -0.116657891 -1.6008483031 0.6481171382 -0.0154397050
## [,14] [,15] [,16] [,17] [,18]
## [1,] -1.389636e-01 0.146484450 0.152780195 0.194313810 0.0045938050
## [2,] 4.588588e-02 0.183284014 0.110494526 -0.539450983 0.3473595954
## [3,] -8.891983e-02 0.037449764 -0.154037553 0.044754210 0.2902846840
## [4,] 4.807221e-02 0.536178956 -0.074295799 0.012890010 -0.8885848353
## [5,] -1.235015e-01 0.020277487 0.041921315 -0.424490630 -0.1466515048
## [6,] -1.205792e+00 -0.436982124 0.084167801 -0.231444184 -0.3582352201
## [7,] 9.228478e-02 0.263316491 -0.023152410 0.190120145 0.0883015898
## [8,] -1.452565e-01 -0.289174719 0.056016470 0.174375517 0.0802790351
## [9,] -6.886671e-01 -0.009842556 0.206759837 0.196786331 0.0541596439
## [10,] -1.470249e-01 -0.457157666 0.146343444 -0.220915542 0.0547708350
## [11,] 2.538375e-01 0.278734157 -0.027435750 0.003256980 -0.0347897982
## [12,] 7.354245e-02 -0.014564148 -0.031559937 0.207406520 0.1126730679
## [13,] -4.916818e-01 0.043534421 -0.102599221 -0.972320505 -1.0900903284
## [14,] 9.403964e-02 0.258676023 0.115337240 -0.391297012 -0.1733574426
## [15,] -3.155707e-01 -1.820939818 -1.105185591 0.174042823 -0.4472031596
## [16,] 6.011780e-01 0.931988582 0.515576407 -0.355808780 -0.8966646929
## [17,] -7.610927e-03 -0.046071389 0.099728759 -0.137436567 0.1192117011
## [18,] -2.903096e-02 0.090226960 0.141171352 -0.099988254 0.0790742941
## [19,] -2.793567e-01 -0.380895127 -0.868655142 0.066304481 0.7310071680
## [20,] 1.840689e-01 0.362725921 -0.255886104 -0.158870079 0.1195451495
## [21,] 2.424412e-01 -0.759436535 -0.254145962 -0.005538412 -0.9342486795
## [22,] -3.354510e-01 -0.828701617 -0.028330332 0.270245828 -0.4773089644
## [23,] 6.694806e-03 -0.013567502 0.059840962 -0.025602561 0.0484249451
## [24,] 1.148030e-01 0.228897610 -0.022111758 0.101811047 0.0291131318
## [25,] 9.384678e-02 -0.889761689 1.104588464 0.506657643 -0.1166833156
## [26,] 6.315381e-03 -0.374817233 0.101131654 -0.207635602 -0.0799188509
## [27,] -1.175436e-01 0.010186101 0.111337602 0.156865497 0.0447312119
## [28,] 7.354245e-02 -0.014564148 -0.031559937 0.207406520 0.1126730679
## [29,] 1.555524e-01 -0.035564472 -0.304441272 -0.001087270 -0.1125755567
## [30,] 1.457293e-01 0.036269044 0.054516969 -0.124156628 -0.0154779849
## [31,] 5.212242e-02 0.121734200 0.009882656 0.244854833 0.0725356610
## [32,] 6.945418e-01 -0.810021884 -0.458250982 0.304915207 -0.6414630534
## [33,] -3.449412e-02 -0.001891250 -0.079860604 0.362931511 0.1215241080
## [34,] -1.906841e-01 -0.424476421 0.105974775 -0.096081878 0.0561683192
## [35,] 7.354245e-02 -0.014564148 -0.031559937 0.207406520 0.1126730679
## [36,] -5.064628e-01 0.660670792 -0.857941198 0.361419548 -1.0366257980
## [37,] 3.104549e-01 -0.290564601 -0.177546504 -0.322076401 0.0343269461
## [38,] -6.853034e-01 1.671039869 0.865175684 0.841226150 -0.3814731120
## [39,] -1.073164e-01 -1.320487286 -0.275191288 0.128133502 -0.2082300314
## [40,] 4.060311e-01 0.306241657 -1.318583141 -0.876885548 0.9743052287
## [41,] 6.249414e-01 -0.106124994 -0.434603365 0.333597836 -0.0419217260
## [42,] -8.580561e-01 0.100630241 0.665680633 0.331178028 0.5784058039
## [43,] 3.617174e-01 0.201866663 0.061201318 0.386485772 -0.5731552343
## [44,] 2.420261e-01 0.059959446 -0.450664208 0.011291099 0.4073514323
## [45,] 2.116728e-01 -0.399695603 0.435312831 -0.448908643 0.3966020138
## [46,] 1.362230e-01 0.092599262 -0.063554351 0.064362733 0.0692505387
## [47,] -1.235015e-01 0.020277487 0.041921315 -0.424490630 -0.1466515048
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## [,19] [,20] [,21] [,22] [,23]
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## [258,] -0.3089808267 0.439624327 -0.6085488220 -0.4043381300 0.034762575
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## [260,] 0.7484275344 -0.403463229 0.1346106412 0.2652496915 -0.629803687
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## [262,] 0.0321922218 -0.053777539 -0.0867306264 -0.1753079280 0.228267904
## [263,] -0.7777404706 -0.081379470 -0.1063657118 0.2096302765 0.162494590
## [264,] 0.0065957932 0.102489525 -0.1944101653 -0.2454251045 0.213308960
## [265,] 0.7484275344 -0.403463229 0.1346106412 0.2652496915 -0.629803687
## [266,] -0.1918704973 0.060887618 0.1376525359 -0.0174187480 -0.434110614
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## [268,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [269,] -0.0339163516 -0.007032311 -0.0363660788 0.0659363154 -0.066044236
## [270,] 0.0321922218 -0.053777539 -0.0867306264 -0.1753079280 0.228267904
## [271,] -0.2253199500 0.490331707 0.8555508506 -1.1318066378 0.453505111
## [272,] 0.0645541175 0.033125900 -0.0790978792 -0.0338010865 -0.144207526
## [273,] 0.2741033047 -0.186453595 -0.1607313795 -0.2085014685 -0.052508588
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## [278,] 0.6619101449 0.124444570 0.1278075631 -0.4561869989 -0.052480151
## [279,] 0.1780397096 0.068617133 0.0312347102 0.2167938587 -0.659847905
## [280,] -0.1753995924 -0.352935324 -0.1000061733 -0.4459635880 0.939969022
## [281,] 0.5412758166 -0.827640572 -0.8292800917 0.0024599721 -0.598481827
## [282,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [283,] 0.0321922218 -0.053777539 -0.0867306264 -0.1753079280 0.228267904
## [284,] -0.4349412051 0.965379415 0.1148165150 0.7069522397 -0.401167140
## [285,] -0.8502606937 0.103400092 -0.1904047929 -0.5182710262 -0.185307354
## [286,] 0.0363754530 0.785664354 0.1132956294 -0.5319265418 0.750968413
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## [290,] 0.0321922218 -0.053777539 -0.0867306264 -0.1753079280 0.228267904
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## [292,] 0.0321922218 -0.053777539 -0.0867306264 -0.1753079280 0.228267904
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## [295,] 0.0321922218 -0.053777539 -0.0867306264 -0.1753079280 0.228267904
## [296,] 0.0321922218 -0.053777539 -0.0867306264 -0.1753079280 0.228267904
## [297,] 1.0871406685 0.445302054 -0.5266316983 0.4781642417 0.280479602
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## [302,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
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## [305,] -1.2753483594 0.303602844 -0.5320765943 -0.3063411594 -0.086768618
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## [308,] 1.2640671141 -0.991929135 1.8427737501 -0.1123951467 -0.411168416
## [309,] 0.0645541175 0.033125900 -0.0790978792 -0.0338010865 -0.144207526
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## [311,] 0.0321922218 -0.053777539 -0.0867306264 -0.1753079280 0.228267904
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## [318,] -0.0396089356 0.183155000 -0.1949546843 0.0685744422 0.369505145
## [319,] -0.5359442393 0.074831552 -0.0808612655 0.4224869730 -0.216758827
## [320,] 0.1571233224 0.193626651 0.0169582265 0.5401003076 0.163007529
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## [322,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
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## [324,] 0.0321922218 -0.053777539 -0.0867306264 -0.1753079280 0.228267904
## [325,] 0.0020593982 -0.092485331 0.0496828402 0.3856527837 0.020850294
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## [328,] 0.0321922218 -0.053777539 -0.0867306264 -0.1753079280 0.228267904
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## [351,] 0.1883089347 0.007507890 -0.2776975231 -0.4053750968 -0.065223851
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## [359,] -0.4141388540 0.163038880 0.0666934896 0.0175164222 -0.433910456
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## [363,] -0.0339163516 -0.007032311 -0.0363660788 0.0659363154 -0.066044236
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## [375,] 0.0465482229 0.205760870 -0.5784081157 -0.3043923611 -0.539765828
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## [379,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [380,] 0.1606964151 -0.196719452 0.1661431782 0.3796557343 0.306376983
## [381,] -0.4537100906 -0.354688274 0.2354509186 0.0942257157 0.144166758
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## [387,] 0.0296783382 -0.901718711 0.7523461601 0.0847301176 -0.330869136
## [388,] 0.1570825611 -0.024362994 0.0877270064 0.2014461075 -0.152992977
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## [394,] -0.0339163516 -0.007032311 -0.0363660788 0.0659363154 -0.066044236
## [395,] 0.4406298176 -0.238246020 -0.1307480731 -0.6057700003 0.127894944
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## [397,] -0.0339163516 -0.007032311 -0.0363660788 0.0659363154 -0.066044236
## [398,] 0.8095256221 1.188626217 -0.0200282209 0.8485075068 -0.417929305
## [399,] -0.1098237517 0.157107350 -0.0766067100 -0.0761598510 0.180420709
## [400,] 0.0176702536 -1.521222049 0.7331854268 0.3863130448 -0.371297065
## [401,] 1.2308372211 1.005336073 0.0591335523 0.5058768767 -0.258208752
## [402,] 0.0876160641 -0.277050428 -0.4726502112 -0.2386889109 0.014445666
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## [404,] -0.5354413730 -0.012915262 -0.2416754973 0.1504432720 0.383963048
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## [407,] 0.3119587216 1.012910295 -0.3075025163 0.0324916655 -0.008238302
## [408,] -0.1507872442 -0.072953909 0.1085624338 -0.7754837197 0.164750842
## [409,] -0.1091523733 -0.111853915 -0.0517185139 -0.1766819209 0.064560637
## [410,] 0.1570825611 -0.024362994 0.0877270064 0.2014461075 -0.152992977
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## [413,] 0.0778974289 -0.746669118 0.0747395539 -0.0270823511 0.761342946
## [414,] -0.0339163516 -0.007032311 -0.0363660788 0.0659363154 -0.066044236
## [415,] 0.1222003613 0.054253118 -0.2273329755 -0.1641308533 -0.359535991
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## [419,] -0.2967805258 0.117247692 0.5929241146 0.5684561482 0.176196649
## [420,] -0.3336849558 0.560997353 -1.0268979341 -0.1636851672 -0.581985071
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## [422,] -0.2650482509 0.087250160 0.1427275369 0.3649619996 -0.485630367
## [423,] -0.1390822921 0.004186933 0.0653503723 -0.1577458808 -0.115495516
## [424,] -0.1560112813 -0.083341581 0.3655812356 -0.3332926135 0.327498999
## [425,] 0.0991242369 0.045000632 -0.0275852797 -0.0101779105 0.204523510
## [426,] -0.7384814555 -0.213453929 0.6302938203 -0.5191805561 -0.273957697
## [427,] -0.0595016271 -0.057241878 0.6907388390 0.3525427418 -0.089251813
## [428,] 0.4153915508 0.293304354 0.2999621197 0.3894922758 0.780469447
## [429,] 0.1053196873 -0.232933493 -0.0298109061 -0.2848597383 0.369696005
## [430,] 0.5293213941 0.488861891 -0.0626900409 0.4154651241 -0.264743749
## [431,] 0.2808373783 -0.049981004 -0.1108726375 -0.1701279028 -0.074009301
## [432,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [433,] 0.0991242369 0.045000632 -0.0275852797 -0.0101779105 0.204523510
## [434,] 0.1606964151 -0.196719452 0.1661431782 0.3796557343 0.306376983
## [435,] -0.1836310522 0.546600012 0.2264594556 0.4467887013 0.084192422
## [436,] -0.2290329554 0.196528190 0.2428427127 0.1649219640 -0.016696977
## [437,] 0.0991242369 0.045000632 -0.0275852797 -0.0101779105 0.204523510
## [438,] 0.1897931650 0.149197161 0.2956307658 0.1984004346 0.144437722
## [439,] -1.1961976495 -0.324381051 0.1579185837 -0.4960758935 -1.153049626
## [440,] 0.7627785798 -0.045978188 -0.0288195793 -0.3825119820 -0.232259309
## [441,] -0.7993729743 0.125042465 0.0427683363 0.8576602524 0.822992433
## [442,] 0.0347102272 0.220423947 0.4436524754 0.2415292036 -0.142277073
## [443,] 0.2546237610 0.253186891 0.9627521642 0.6135966556 -0.148826477
## [444,] -0.0172953081 0.099618457 0.0902181756 0.1590873430 0.171635259
## [445,] 0.0494846437 -0.216088037 0.0647418241 -0.1826789703 0.350087327
## [446,] 0.1318348408 0.218560787 0.1803184797 -0.0132235834 0.501954209
## [447,] 0.2222859586 0.346226274 0.2966643052 0.0321260994 0.119638664
## [448,] 0.0369815652 -0.251907033 -0.0323244716 -0.0562516760 0.493486244
## [449,] -0.2147344305 0.155694685 -0.2857247678 -0.2980073886 -0.295725354
## [450,] -0.1390822921 0.004186933 0.0653503723 -0.1577458808 -0.115495516
## [451,] 0.3165311005 0.134109106 -0.7898095288 0.7305072038 -1.063352199
## [452,] -0.0981352178 -0.128425327 0.3557039115 0.2861066738 -0.194240163
## [453,] -0.4257809756 -1.274553248 -0.4776413638 0.0568710890 0.580114999
## [454,] -0.1390822921 0.004186933 0.0653503723 -0.1577458808 -0.115495516
## [455,] -0.1503358965 0.047585513 0.0814373765 0.2352015689 -0.098932487
## [456,] 0.0344212939 -0.005581891 0.0573155874 0.5271596252 -0.351625136
## [457,] 0.0369815652 -0.251907033 -0.0323244716 -0.0562516760 0.493486244
## [458,] 0.0402467110 -0.510920207 -0.1541793120 0.2665104653 0.282950074
## [459,] -0.1390822921 0.004186933 0.0653503723 -0.1577458808 -0.115495516
## [460,] 0.0991242369 0.045000632 -0.0275852797 -0.0101779105 0.204523510
## [461,] 0.1570825611 -0.024362994 0.0877270064 0.2014461075 -0.152992977
## [462,] -0.2555018370 0.058804758 0.1831538276 0.0115193727 -0.148383767
## [463,] -0.1390822921 0.004186933 0.0653503723 -0.1577458808 -0.115495516
## [464,] -0.2710299090 -0.041566662 0.1519046139 0.1906125495 0.269170688
## [465,] -0.5898937250 0.227984496 -0.0998983263 -0.6099314629 -0.408332512
## [466,] 0.1350999866 -0.040452387 0.0584636393 0.3095385578 0.291418039
## [467,] 0.3229288626 0.204242298 0.4495865342 -0.1562309588 0.237699398
## [468,] 0.3995453003 0.201240548 0.6658361969 -1.0339171004 0.612107458
## [469,] 0.4982730320 -0.409976800 -0.0183752283 0.2026248453 -0.313813915
## [470,] -0.0172953081 0.099618457 0.0902181756 0.1590873430 0.171635259
## [471,] 0.4513673005 0.207851334 0.3860110387 0.7092087441 0.867363976
## [472,] 0.0344212939 -0.005581891 0.0573155874 0.5271596252 -0.351625136
## [473,] -0.3388121403 0.390673548 -0.2129657069 0.4635651973 -0.174656792
## [474,] 0.4675047419 0.489627936 0.2190192253 -0.2596783248 -0.018664562
## [475,] 0.8801472839 -0.495571314 -0.2319324526 -0.0362712039 -0.503878182
## [476,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [477,] 0.1239191812 0.222303920 0.7304002733 -0.0513645372 -0.219751557
## [478,] -0.2617435593 0.022968036 0.0349389533 0.1679676369 -0.314127676
## [479,] -0.1628921001 -0.075093167 0.1960107954 0.4767346838 -0.606779191
## [480,] -0.2030213617 0.428838537 0.3196426565 -0.2431566215 0.248382177
## [481,] 0.0344212939 -0.005581891 0.0573155874 0.5271596252 -0.351625136
## [482,] 0.1606964151 -0.196719452 0.1661431782 0.3796557343 0.306376983
## [483,] -0.5092364379 -0.082380360 0.2448402659 0.0430445793 -0.050848339
## [484,] -0.2977193090 0.108421055 -0.0511099657 -0.1517488314 -0.401022206
## [485,] -0.2977193090 0.108421055 -0.0511099657 -0.1517488314 -0.401022206
## [486,] -0.0882574824 -0.367978294 -0.4070531166 -0.2884531971 0.204840995
## [487,] -0.2977193090 0.108421055 -0.0511099657 -0.1517488314 -0.401022206
## [488,] -0.2119249390 -0.085540430 0.0658561779 0.0451247968 -0.388306943
## [489,] -0.2316107357 0.061675827 -0.1014745133 -0.3929930748 -0.106710066
## [490,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [491,] 0.4594295971 -0.009106183 0.1098120228 -0.0202886735 -0.089914745
## [492,] 0.3474827609 -0.240128231 -0.2062956632 0.4368123711 0.168397414
## [493,] 0.4147913576 -0.270926505 0.1638416869 0.1461877254 -0.109037704
## [494,] 0.0991242369 0.045000632 -0.0275852797 -0.0101779105 0.204523510
## [495,] 0.2808373783 -0.049981004 -0.1108726375 -0.1701279028 -0.074009301
## [496,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [497,] -0.0595127801 0.149234753 -0.1440456177 -0.0041808611 -0.081003179
## [498,] 0.0991242369 0.045000632 -0.0275852797 -0.0101779105 0.204523510
## [499,] 0.0344212939 -0.005581891 0.0573155874 0.5271596252 -0.351625136
## [500,] 0.1164275216 -0.078973971 -0.2779739094 0.3682551251 0.186680580
## [501,] 0.0731982297 0.317232587 -0.3937691966 0.1547242651 -0.609997159
## [502,] 0.1606964151 -0.196719452 0.1661431782 0.3796557343 0.306376983
## [503,] 0.0020593982 -0.092485331 0.0496828402 0.3856527837 0.020850294
## [504,] 0.1264573861 -0.163706654 0.3224966052 0.5675849893 -0.173165965
## [505,] -0.0126957701 0.261832831 0.1903070285 -0.1189157831 0.255910616
## [506,] 0.3043148308 -0.122520428 0.1400623010 0.0692899678 -0.001845785
## [507,] 0.0405118734 -0.007067061 0.1253184141 -0.1483951790 -0.336823755
## [508,] -0.1156855403 0.716538591 0.7445615904 0.0586614420 -0.336627418
## [509,] -0.2992034526 -0.399697023 0.1104878105 -0.4629972275 0.058278122
## [510,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [511,] 0.2428769311 -0.218324478 0.2046931499 0.3983197357 -0.140277714
## [512,] -0.1390822921 0.004186933 0.0653503723 -0.1577458808 -0.115495516
## [513,] -0.2316107357 0.061675827 -0.1014745133 -0.3929930748 -0.106710066
## [514,] 0.0404257381 -0.880517341 -0.0309349836 -0.0288334346 0.354334624
## [515,] -0.2617435593 0.022968036 0.0349389533 0.1679676369 -0.314127676
## [516,] -0.5900099886 -0.173087326 0.0736316613 0.1465017935 0.172470895
## [517,] -0.7842929998 0.076471586 0.2461833831 0.2183068822 -0.369263279
## [518,] 0.0681679715 -0.139230559 -0.0006817074 0.1444085403 0.315162433
## [519,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [520,] 0.1222003613 0.054253118 -0.2273329755 -0.1641308533 -0.359535991
## [521,] 0.0683469986 -0.508827693 0.1225626210 -0.1509353596 0.386546983
## [522,] 0.0065957932 0.102489525 -0.1944101653 -0.2454251045 0.213308960
## [523,] -0.1098237517 0.157107350 -0.0766067100 -0.0761598510 0.180420709
## [524,] -0.2977193090 0.108421055 -0.0511099657 -0.1517488314 -0.401022206
## [525,] -0.1543660557 -0.321233066 -0.3566885690 -0.0472089536 -0.089471145
## [526,] -0.0789137582 0.027567693 -0.2539507830 -0.3489798654 0.069210372
## [527,] 0.1570825611 -0.024362994 0.0877270064 0.2014461075 -0.152992977
## [528,] 0.4014712729 0.060257442 -0.0055002632 -0.2319126916 0.267601741
## [529,] -0.2977193090 0.108421055 -0.0511099657 -0.1517488314 -0.401022206
## [530,] 0.1583551382 -0.400797036 -0.0180397281 -0.1397582849 -0.201256911
## [531,] -0.0595127801 0.149234753 -0.1440456177 -0.0041808611 -0.081003179
## [532,] -0.2169308501 -0.658709189 -0.2109356259 -0.1768341355 0.085937197
## [533,] 0.3168131280 -0.135434023 -0.0248237185 0.1495885656 0.012885228
## [534,] 0.1930583108 -0.109816013 0.1737759254 0.5211625758 -0.066098447
## [535,] 0.2787573609 -0.313914970 -0.1442894499 0.0736240744 0.666898533
## [536,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [537,] 0.0321922218 -0.053777539 -0.0867306264 -0.1753079280 0.228267904
## [538,] -0.0990649243 -0.067830891 -0.1243968041 0.6019191070 -0.469023935
## [539,] -0.7520101421 0.646105690 0.3283939746 0.3790057923 -0.122422267
## [540,] 0.1570825611 -0.024362994 0.0877270064 0.2014461075 -0.152992977
## [541,] 0.5101842403 -0.168785809 -0.1819840008 -0.2177680712 -0.139997051
## [542,] -0.4243163512 -0.162129219 0.3562627937 0.8824649491 0.050365540
## [543,] 0.1318348408 0.218560787 0.1803184797 -0.0132235834 0.501954209
## [544,] 0.1222003613 0.054253118 -0.2273329755 -0.1641308533 -0.359535991
## [545,] -0.0595127801 0.149234753 -0.1440456177 -0.0041808611 -0.081003179
## [546,] 0.0065957932 0.102489525 -0.1944101653 -0.2454251045 0.213308960
## [547,] 0.0065957932 0.102489525 -0.1944101653 -0.2454251045 0.213308960
## [548,] 0.0321922218 -0.053777539 -0.0867306264 -0.1753079280 0.228267904
## [549,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [550,] -0.3072628741 0.213183579 -0.4525496534 -0.5332545825 -0.286939904
## [551,] 0.1840354018 0.036985024 0.4520258528 -0.3165058596 -0.170241575
## [552,] -0.0518654275 0.087743725 0.0387055761 0.1354641670 -0.177095777
## [553,] -0.0397590275 0.339431687 -0.0391458647 0.1808498513 -0.137465911
## [554,] -0.9019410700 0.156555356 0.0675387126 0.5720534791 -0.685176428
## [555,] -0.6054730253 0.390974492 0.7924748700 -0.5774625766 -0.435733523
## [556,] -0.3679660599 0.355947505 -0.0135816869 0.3258294014 0.009596435
## [557,] 0.5754637796 -0.045382995 -0.4210705303 0.3655696300 -0.415652778
## [558,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [559,] -0.0339163516 -0.007032311 -0.0363660788 0.0659363154 -0.066044236
## [560,] -0.9278410282 0.788818714 0.0203760560 -0.2000984064 0.182448467
## [561,] -0.1098237517 0.157107350 -0.0766067100 -0.0761598510 0.180420709
## [562,] -0.0595127801 0.149234753 -0.1440456177 -0.0041808611 -0.081003179
## [563,] -0.0339163516 -0.007032311 -0.0363660788 0.0659363154 -0.066044236
## [564,] -0.0339163516 -0.007032311 -0.0363660788 0.0659363154 -0.066044236
## [565,] 0.0321922218 -0.053777539 -0.0867306264 -0.1753079280 0.228267904
## [566,] -0.1759323251 0.203852578 -0.0262421624 0.1650843924 -0.113891430
## [567,] 0.7641098758 0.770244791 0.0301422631 0.3963239828 -0.084515281
## [568,] 0.2063133333 -1.144034669 -0.4861682616 0.2633728622 -0.144071414
## [569,] 0.1570825611 -0.024362994 0.0877270064 0.2014461075 -0.152992977
## [570,] 0.6879584111 0.384627769 0.0537702971 0.4094680747 0.020782941
## [571,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [572,] -0.5300348353 -0.606610969 0.6307670164 -0.2364383452 -0.642108970
## [573,] -0.1351649185 0.300742505 -0.4951207578 -0.1444423689 -0.261233017
## [574,] -0.0923657719 -0.407502184 -0.9121532368 1.1196574078 0.776439982
## [575,] 0.0991242369 0.045000632 -0.0275852797 -0.0101779105 0.204523510
## [576,] -0.5514588734 -0.376392435 0.0265524187 -0.7537430200 -0.313885280
## [577,] -0.1517485597 -0.003148127 -0.2512751139 -0.0666228784 0.301452599
## [578,] 0.5234954223 0.222344997 -0.4931514094 -0.2907169058 -0.557790328
## [579,] -0.0172953081 0.099618457 0.0902181756 0.1590873430 0.171635259
## [580,] -0.3415043285 -0.315890102 0.3329334598 -0.3390113465 0.056002220
## [581,] -0.0595127801 0.149234753 -0.1440456177 -0.0041808611 -0.081003179
## [582,] -0.4141388540 0.163038880 0.0666934896 0.0175164222 -0.433910456
## [583,] -0.0430437999 -0.158599143 -0.1020830615 -0.4179261643 0.358872777
## [584,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [585,] -0.4749786407 0.058607369 0.1748900163 0.4916775001 0.357748669
## [586,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [587,] 0.0020593982 -0.092485331 0.0496828402 0.3856527837 0.020850294
## [588,] -0.2977193090 0.108421055 -0.0511099657 -0.1517488314 -0.401022206
## [589,] -0.4558730926 0.083503571 0.0530413947 0.2229944537 0.122482939
## [590,] 0.1196636853 0.503923329 0.3310838233 0.3755103414 0.058996765
## [591,] 0.0696249296 0.578366891 0.1536582758 0.1233759696 -0.045722636
## [592,] -0.0532879220 -0.189774551 0.1823165159 0.0391277474 -0.102780253
## [593,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [594,] -0.1890681159 0.284708436 0.5467533798 -0.6509586818 -0.013869645
## [595,] 0.0991242369 0.045000632 -0.0275852797 -0.0101779105 0.204523510
## [596,] -0.3888933352 -0.126629876 0.2853213839 0.2652047125 -0.452970163
## [597,] 0.3033215699 0.643562001 0.2512571205 -0.5654743538 -0.182296612
## [598,] -0.3598003511 -0.977780393 0.6425107545 -0.5384148925 -0.536254009
## [599,] 0.4245473974 0.069509928 -0.2052479591 -0.3858656344 -0.296457759
## [600,] 0.1581761111 -0.031199902 -0.1412840565 0.1555856150 -0.272641461
## [601,] -0.3473589022 -0.152667614 0.0412171381 -0.3242498912 -0.255458389
## [602,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [603,] -0.2977193090 0.108421055 -0.0511099657 -0.1517488314 -0.401022206
## [604,] -0.0595127801 0.149234753 -0.1440456177 -0.0041808611 -0.081003179
## [605,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [606,] 0.4679295571 -0.983408093 0.1530848915 -0.4669342353 0.324220735
## [607,] -0.0293902906 0.296463014 0.1579576249 0.1005617765 -0.043181400
## [608,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [609,] 0.0622573396 -0.130179751 0.0589694448 0.5124092354 0.018606613
## [610,] 0.5771078256 -0.456365729 0.3237695797 0.1245442090 -0.557277556
## [611,] -0.7816939936 -0.349708701 -1.7039745292 0.1514414268 0.121346293
## [612,] 0.3460407758 0.320608264 0.0980646613 -0.3394479109 0.198622339
## [613,] 0.2808373783 -0.049981004 -0.1108726375 -0.1701279028 -0.074009301
## [614,] -0.1390822921 0.004186933 0.0653503723 -0.1577458808 -0.115495516
## [615,] -0.4155227778 -0.773123149 0.0315887664 -0.0249166028 0.406266539
## [616,] -0.0595127801 0.149234753 -0.1440456177 -0.0041808611 -0.081003179
## [617,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [618,] 0.2705736627 0.313712282 0.5800014669 0.4748598875 0.549976193
## [619,] 0.1570825611 -0.024362994 0.0877270064 0.2014461075 -0.152992977
## [620,] -0.0828419204 0.161264056 0.0246634898 0.1827945897 -0.151309524
## [621,] -0.6561854980 0.843996879 -0.8405559233 0.0125510353 -0.391507926
## [622,] -0.8944883105 0.259373905 0.1633150054 -0.3174545662 0.112952675
## [623,] -0.1390822921 0.004186933 0.0653503723 -0.1577458808 -0.115495516
## [624,] 0.1318348408 0.218560787 0.1803184797 -0.0132235834 0.501954209
## [625,] -0.1063716881 0.177747088 0.2732541317 -0.1607915537 0.181935183
## [626,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [627,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [628,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [629,] 0.2808373783 -0.049981004 -0.1108726375 -0.1701279028 -0.074009301
## [630,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [631,] -0.3618530254 -0.143215902 0.3773876081 0.4299949796 0.251241380
## [632,] 0.1574312693 0.062293722 0.2879980186 0.0568935931 0.516913152
## [633,] 0.1154015729 -0.184977026 0.3652961670 -1.2710501954 0.291489970
## [634,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [635,] 0.7125417888 -0.389238545 0.3484086194 0.4939188970 -0.690126110
## [636,] -0.3713598935 0.079960550 0.3510275742 0.2636811026 0.296033641
## [637,] -0.1351649185 0.300742505 -0.4951207578 -0.1444423689 -0.261233017
## [638,] -0.2977193090 0.108421055 -0.0511099657 -0.1517488314 -0.401022206
## [639,] 0.0645541175 0.033125900 -0.0790978792 -0.0338010865 -0.144207526
## [640,] -0.0015544559 0.079871128 -0.0287333316 0.2074431569 -0.438519666
## [641,] -0.0595127801 0.149234753 -0.1440456177 -0.0041808611 -0.081003179
## [642,] -0.4863317331 -0.118440340 -0.3617832382 0.3497605752 0.395287144
## [643,] 0.4476769581 -0.145809216 -1.2102375812 0.0072859136 -0.708708162
## [644,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [645,] -0.0339163516 -0.007032311 -0.0363660788 0.0659363154 -0.066044236
## [646,] -0.2316107357 0.061675827 -0.1014745133 -0.3929930748 -0.106710066
## [647,] -0.0835559447 -0.268120980 0.0559610250 -0.1065647444 0.079519581
## [648,] -0.0835559447 -0.268120980 0.0559610250 -0.1065647444 0.079519581
## [649,] 0.0311561481 0.253431283 0.1791704278 0.2043974840 -0.141088967
## [650,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [651,] -0.3478598128 -0.100244847 0.3861296937 0.8707509780 0.405193884
## [652,] 0.0645541175 0.033125900 -0.0790978792 -0.0338010865 -0.144207526
## [653,] -0.2406536338 0.209007082 -0.7778506356 0.3004603079 0.029143083
## [654,] -0.0636841178 0.429038822 0.3037467627 -0.0421598625 0.103037642
## [655,] -0.6478026910 0.784745065 0.3655604860 -0.2972143214 -0.315619370
## [656,] -0.2198056584 -0.247402878 0.2173581579 0.3638630018 -0.066845086
## [657,] 0.1883089347 0.007507890 -0.2776975231 -0.4053750968 -0.065223851
## [658,] 0.4646458934 0.103621273 0.1722712338 -0.0532967362 0.013385252
## [659,] -0.0339163516 -0.007032311 -0.0363660788 0.0659363154 -0.066044236
## [660,] -0.3790067736 0.189813983 0.0022868558 -0.1763973986 -0.113812064
## [661,] -0.1503358965 0.047585513 0.0814373765 0.2352015689 -0.098932487
## [662,] 0.0991242369 0.045000632 -0.0275852797 -0.0101779105 0.204523510
## [663,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [664,] 0.2808373783 -0.049981004 -0.1108726375 -0.1701279028 -0.074009301
## [665,] -0.0307630506 -0.166582934 0.6846350399 0.0061394152 -0.465961294
## [666,] -0.6285125252 -0.033921920 -0.2091292468 -0.1783660670 0.577856026
## [667,] -0.0690563452 0.253997277 -0.5454853054 -0.3856866123 0.033079122
## [668,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [669,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [670,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [671,] 0.1247206654 -0.111266433 0.0800942592 0.0599392660 0.219482453
## [672,] -0.1734384073 0.191073250 0.0668914952 0.2191883529 -0.375700806
## [673,] -0.1390822921 0.004186933 0.0653503723 -0.1577458808 -0.115495516
## [674,] 0.2770363816 -0.314902041 0.8160033180 -0.3230940622 0.259014835
## [675,] 0.1574312693 0.062293722 0.2879980186 0.0568935931 0.516913152
## [676,] 0.2826069530 0.516806166 -0.0970999746 -0.8574676374 0.516253557
## [677,] 0.1570825611 -0.024362994 0.0877270064 0.2014461075 -0.152992977
## [678,] -0.0477591847 0.160536602 -0.0292778506 0.5214427036 -0.282323481
## [679,] 0.3172757484 -0.157284049 0.0377898829 -0.1340021949 -0.224107664
## [680,] 0.2808373783 -0.049981004 -0.1108726375 -0.1701279028 -0.074009301
## [681,] 0.4528945748 1.169861743 -0.3788482615 0.8891812797 0.734126710
## [682,] -0.2501528114 -0.553383229 1.0039160238 -0.7550992193 -0.886971413
## [683,] -0.3689824494 0.139614158 0.4021793636 -1.5257446772 -0.079359252
## [,24] [,25] [,26] [,27] [,28]
## [1,] -0.023870906 -0.2533762299 0.060457998 0.097935932 -0.030603065
## [2,] -0.734807029 0.0536516959 -0.133515096 1.282100078 -0.396582018
## [3,] -0.042387890 -0.7096277444 -0.006793177 -0.281299221 -0.465836655
## [4,] 0.522366075 -0.2001565386 -0.335246573 0.127504221 -0.276401059
## [5,] -0.259186950 -0.3030214681 -0.047545892 -0.053492687 0.207683314
## [6,] 0.517170481 0.4928020473 0.969483524 1.372102760 -1.149202990
## [7,] 0.036512316 -0.1295981594 -0.102299087 0.220646090 -0.209412323
## [8,] -0.110976507 0.1216312254 0.289399359 -0.147099555 0.100490940
## [9,] -0.489072424 0.9632167877 0.920840864 -0.418364621 0.158732337
## [10,] -0.104260180 0.1098541111 -0.307757594 -0.073090989 0.402720550
## [11,] 0.238664209 -0.0341451650 -0.456332573 0.194267031 -0.420041224
## [12,] -0.114007166 0.1532870821 0.395142814 -0.259196287 0.080682723
## [13,] 0.319201024 0.1958002999 0.208092648 -0.129411639 -0.163797518
## [14,] 0.158357289 -0.2189931319 -0.408828945 0.089887101 -0.566215726
## [15,] 0.061009314 -0.3176369973 -0.511175376 0.107447198 -0.312449234
## [16,] -0.098598534 0.0750372533 0.431666352 0.142971252 0.270744129
## [17,] -0.117550435 -0.0007865872 0.040374971 -0.198187052 0.222639665
## [18,] -0.112717010 -0.1014343356 -0.059514155 -0.044993530 0.127094537
## [19,] -0.150613784 -0.2751729659 -0.064137046 -0.571733476 0.031836876
## [20,] 0.090631379 -0.1451354783 -0.016376134 -0.175802417 0.162670813
## [21,] 0.118125181 0.8189205963 -0.295000240 -0.172516804 -0.416562238
## [22,] 0.319905194 -0.4429985171 -1.151641353 0.170536275 0.246439297
## [23,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [24,] 0.047040059 -0.1394898905 -0.138522724 0.185136766 -0.152831092
## [25,] -0.579381021 -0.1770551337 -1.140255927 0.626232544 0.332025567
## [26,] 0.113634617 0.1336423200 -0.592855239 -0.269655898 -0.089557308
## [27,] -0.028704331 -0.1527284815 0.160347123 -0.055257590 0.064942064
## [28,] -0.114007166 0.1532870821 0.395142814 -0.259196287 0.080682723
## [29,] 0.324169704 0.1486729796 0.021044669 0.511455342 0.150006774
## [30,] 0.100344363 0.0230016217 -0.244722674 -0.394751960 -0.269638193
## [31,] -0.109173740 0.0526393337 0.295253688 -0.106002765 -0.014862406
## [32,] 0.049121687 0.2022624292 0.059662061 -1.312948675 0.801642457
## [33,] -0.101858049 0.0595299291 0.436274235 -0.016241110 -0.205260857
## [34,] -0.093082554 -0.0133512120 0.067232846 -0.444979015 0.112925285
## [35,] -0.114007166 0.1532870821 0.395142814 -0.259196287 0.080682723
## [36,] -0.183693865 0.0537629239 0.299432862 0.124018809 0.111671962
## [37,] 0.313540495 0.2380725450 -0.465755112 0.040058029 0.215544592
## [38,] -0.686327980 0.1834504251 0.615906495 0.133231800 -0.171629830
## [39,] 0.644875721 -0.3767509584 -0.368889163 0.194683899 0.617559651
## [40,] 1.178878565 -0.3516417461 -0.180390275 -0.187185854 -0.236351204
## [41,] -0.277001701 0.1170510356 0.447545846 0.017653922 0.803604430
## [42,] 0.290613335 -0.8608805199 -0.496353632 0.133806429 0.126061313
## [43,] -0.771941237 -0.2216764549 -0.048501273 -0.055363776 0.550505138
## [44,] 0.160992503 0.2025385482 0.076433464 -0.079869995 -0.171077897
## [45,] -0.629844999 -0.6261891527 0.524982949 -1.054463203 0.810491383
## [46,] 0.042206634 -0.0388421421 -0.038633598 0.031943244 -0.057285963
## [47,] -0.259186950 -0.3030214681 -0.047545892 -0.053492687 0.207683314
## [48,] 0.184738026 0.0797408995 0.422336122 0.405159893 -0.209387867
## [49,] -0.461696409 0.5897743894 -0.324710381 -0.939213721 -0.189689964
## [50,] 0.394408604 0.3205115569 0.060643007 -0.267774701 0.333508974
## [51,] 0.370307861 0.7098679030 1.020747056 -0.395090672 -0.345067391
## [52,] 0.984293844 0.6127453325 0.192267229 0.744178251 -1.147314716
## [53,] 0.211112074 -0.3224540600 -0.617954091 0.134493392 0.177130333
## [54,] -0.561559361 -0.5800157139 0.457624867 -0.529682759 0.025369586
## [55,] -0.926063148 1.6862959842 -0.501492946 -0.717024868 0.083918159
## [56,] 0.193556218 0.4741982033 -0.839036558 -0.095580736 0.034354113
## [57,] 0.684181977 -0.1361702848 -0.174370790 0.278950592 0.213566298
## [58,] 0.153416377 -0.4951128672 -0.643573472 -0.334412354 -0.517039603
## [59,] 0.196738880 0.4538104022 -0.574758894 0.217582549 -0.272960396
## [60,] 0.086265105 -0.5654790344 -0.018624826 0.001332726 -0.425149429
## [61,] -0.149699225 0.4578781242 -0.422110942 0.300507172 0.214099122
## [62,] -0.146429890 -0.0716086514 -0.052296040 -0.400198958 -0.125074704
## [63,] 0.042206634 -0.0388421421 -0.038633598 0.031943244 -0.057285963
## [64,] 0.394465201 -0.5629492746 0.167038804 -0.055292217 -0.120566575
## [65,] -0.112717010 -0.1014343356 -0.059514155 -0.044993530 0.127094537
## [66,] -0.531128358 0.1260123457 0.259157778 -0.287604053 0.454956264
## [67,] -1.739396357 -0.0257798199 0.281181813 -0.590066405 0.032267556
## [68,] -0.355858250 -0.3285573970 -0.143575716 0.368585727 -0.421346342
## [69,] 0.210899710 -0.1363468170 0.277238178 0.175762703 0.170207428
## [70,] 1.065158349 -0.9732618741 0.797973162 0.134276060 0.572775189
## [71,] -0.028544578 0.0620813181 0.571002534 0.786150175 -0.424468447
## [72,] -0.043349164 -0.5026445505 -0.180531753 0.525399121 0.881410649
## [73,] -0.055750661 -0.4959490020 -0.541568869 -0.058840913 0.499926741
## [74,] -0.401574729 -0.6322512897 0.006955194 0.395299678 -0.437732386
## [75,] 0.154485338 -0.1012590602 -0.061831964 -0.005213843 0.126556024
## [76,] 0.041010587 0.0543059695 0.541470882 0.049652444 -0.183448433
## [77,] 0.024870869 -0.2624940935 -0.297108171 -0.345938368 -0.511357823
## [78,] -0.052405930 0.3376806001 0.317562159 -0.359508604 -0.121301108
## [79,] 0.111932609 0.5048392487 -0.159979619 0.068760891 0.153364719
## [80,] -0.110234744 0.0061040082 0.181395517 -0.108425397 0.032241214
## [81,] -0.010580651 -0.1427355316 -0.287674567 0.223031994 0.149477820
## [82,] -0.024393178 -0.5424051448 0.209770259 -0.199665102 -0.325833627
## [83,] 0.243832392 -0.3506271688 0.659269239 -1.222668513 -0.880037580
## [84,] 0.486725070 -0.3899519788 -0.139745239 -0.340295627 0.615404389
## [85,] -0.040451305 0.9579726467 0.092848418 -0.387881369 -0.015155115
## [86,] 0.106684201 -1.2197020819 0.080384906 -0.327652311 1.012735253
## [87,] -0.112717010 -0.1014343356 -0.059514155 -0.044993530 0.127094537
## [88,] -0.045090238 0.3445711954 0.458582706 -0.269746949 -0.311699559
## [89,] 0.047040059 -0.1394898905 -0.138522724 0.185136766 -0.152831092
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## [171,] -0.109173740 0.0526393337 0.295253688 -0.106002765 -0.014862406
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## [173,] -0.112717010 -0.1014343356 -0.059514155 -0.044993530 0.127094537
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## [178,] 0.484405246 -0.3493877952 0.638437698 1.252945672 0.470376787
## [179,] -0.297456624 -0.0370845092 0.007184057 -0.706616984 -0.083219986
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## [181,] 0.360694822 0.0487554951 -0.886311144 0.340883057 -0.141808186
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## [185,] 0.843095468 0.1226471552 0.346851756 0.493293061 0.069801025
## [186,] -0.031090564 0.3612466732 -0.482087503 -0.032836776 0.313500928
## [187,] -0.028704331 -0.1527284815 0.160347123 -0.055257590 0.064942064
## [188,] 0.047040059 -0.1394898905 -0.138522724 0.185136766 -0.152831092
## [189,] -0.086446361 -0.1829908521 -0.026801950 -0.250688703 -0.097973189
## [190,] -0.112717010 -0.1014343356 -0.059514155 -0.044993530 0.127094537
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## [193,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
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## [195,] -0.484151072 0.3087626797 -0.580294075 0.135808307 1.384822898
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## [197,] 0.047040059 -0.1394898905 -0.138522724 0.185136766 -0.152831092
## [198,] -0.023870906 -0.2533762299 0.060457998 0.097935932 -0.030603065
## [199,] 0.047040059 -0.1394898905 -0.138522724 0.185136766 -0.152831092
## [200,] -0.574832497 0.9616219317 1.630994844 -0.249232151 0.126400269
## [201,] 0.704742431 -0.3990152200 0.915087021 0.618847356 -0.074022058
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## [203,] 0.238664209 -0.0341451650 -0.456332573 0.194267031 -0.420041224
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## [221,] -0.978104467 0.0949416154 -0.297134053 -0.663617339 -0.183137000
## [222,] 0.173700511 -0.4472393913 1.064818039 0.186247792 -0.935190730
## [223,] 0.238664209 -0.0341451650 -0.456332573 0.194267031 -0.420041224
## [224,] 0.342188474 0.2625600619 -0.022740912 0.521748013 0.187308381
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## [238,] 0.047040059 -0.1394898905 -0.138522724 0.185136766 -0.152831092
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## [270,] 0.047040059 -0.1394898905 -0.138522724 0.185136766 -0.152831092
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## [272,] -0.086446361 -0.1829908521 -0.026801950 -0.250688703 -0.097973189
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## [280,] 0.666898596 -0.0321527033 0.484999177 -0.738075356 0.231797365
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## [282,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [283,] 0.047040059 -0.1394898905 -0.138522724 0.185136766 -0.152831092
## [284,] 0.016956820 -0.5236362615 0.126442219 0.181393782 0.237802086
## [285,] 0.951620996 0.0566210708 0.291498630 -0.523401883 -0.336568273
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## [287,] -0.097415845 0.4281655288 -0.430613860 0.327973769 0.254287147
## [288,] -0.099821728 -0.4488212766 0.294770698 -0.310868447 -0.251994003
## [289,] -0.341399869 0.1839194743 -0.306753712 0.081880900 0.549520875
## [290,] 0.047040059 -0.1394898905 -0.138522724 0.185136766 -0.152831092
## [291,] 0.531972985 0.2294514867 -0.206871003 -0.843412380 -0.710389394
## [292,] 0.047040059 -0.1394898905 -0.138522724 0.185136766 -0.152831092
## [293,] -0.238841749 0.7094975138 1.062804710 0.031467110 -0.375878544
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## [295,] 0.047040059 -0.1394898905 -0.138522724 0.185136766 -0.152831092
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## [330,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
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## [332,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
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## [345,] -0.269630908 -0.3984025621 -0.595364683 -0.249490968 1.164084782
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## [362,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
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## [367,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
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## [372,] -0.308606673 0.3631346531 0.172833473 -0.036978115 -0.082155559
## [373,] -0.203781199 -0.2498245364 0.422762177 -0.104926783 0.109995476
## [374,] 0.347049290 0.1544334036 0.480892157 0.333553942 -0.375712028
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## [378,] -0.398085256 0.4653450575 -0.093957650 -0.145270201 -0.216415236
## [379,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [380,] 0.276189812 0.2376360404 -0.413656235 0.289565312 -0.222468724
## [381,] 0.295100930 0.0881802208 -0.269875109 0.388059600 0.228060286
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## [386,] 0.337459959 0.2593136779 -0.327087896 0.636551404 0.330087658
## [387,] 0.077587867 0.5243587555 0.504891690 -0.166534289 -0.062051661
## [388,] -0.048920758 0.0887903534 0.015874389 -0.155390421 0.099599312
## [389,] 0.273298937 0.0637970386 0.517341390 0.190911083 0.112215383
## [390,] 0.039411555 0.0501421049 -0.246637294 -0.249547728 0.383556768
## [391,] -0.451512332 -0.1477226257 -0.437063679 0.580480914 0.036895820
## [392,] 0.042206634 -0.0388421421 -0.038633598 0.031943244 -0.057285963
## [393,] -0.106062948 0.1788460028 -0.313611924 -0.114187780 0.518073895
## [394,] 0.042206634 -0.0388421421 -0.038633598 0.031943244 -0.057285963
## [395,] 0.002796882 -0.1979712159 0.690531890 -0.072800040 -0.515763023
## [396,] -0.093082554 -0.0133512120 0.067232846 -0.444979015 0.112925285
## [397,] 0.042206634 -0.0388421421 -0.038633598 0.031943244 -0.057285963
## [398,] -0.256311881 -0.9042800324 -0.318651795 -0.007077874 1.015923088
## [399,] -0.025673673 -0.1843843382 0.054603668 0.056839141 0.084750281
## [400,] -0.247552096 -0.1125306309 -0.180213851 -0.558657101 -0.728162692
## [401,] 0.522666479 -0.4895208885 -0.263430734 -0.505523054 -0.371075133
## [402,] -0.477451383 0.3822005755 -0.669616940 0.379107056 0.051352781
## [403,] 0.042206634 -0.0388421421 -0.038633598 0.031943244 -0.057285963
## [404,] -0.245121695 -0.5411767531 -0.022485508 0.312722061 -0.675737936
## [405,] -0.053093065 0.6799672161 0.450006476 0.136092594 0.135362442
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## [407,] -0.715622762 0.2571608657 0.168683378 0.483613833 -0.371288480
## [408,] 0.174259010 0.1994248148 0.433584832 0.315833365 0.150171747
## [409,] 0.210899710 -0.1363468170 0.277238178 0.175762703 0.170207428
## [410,] -0.048920758 0.0887903534 0.015874389 -0.155390421 0.099599312
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## [412,] -0.016309217 0.1859823380 0.504684605 0.143886557 0.069739489
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## [414,] 0.042206634 -0.0388421421 -0.038633598 0.031943244 -0.057285963
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## [420,] -1.029060243 -0.1162744035 -0.391904263 0.467527454 -0.297560988
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## [422,] 0.056532210 -0.2374673466 0.541142214 0.405650663 0.731263589
## [423,] -0.075191407 0.1703468699 -0.016837816 0.050304752 0.324667037
## [424,] 0.017942694 -0.0148585980 0.112021501 0.272825888 0.510521179
## [425,] 0.013654698 0.0184049756 0.103134336 0.193234213 0.166969436
## [426,] 0.090375054 -0.1516788370 -0.156257153 0.057855560 -0.255010262
## [427,] -0.022775129 0.1956095566 -0.520263690 0.133542860 0.863038377
## [428,] 0.049412952 -0.1487990589 -0.354184343 0.176686225 -0.288054449
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## [432,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [433,] 0.013654698 0.0184049756 0.103134336 0.193234213 0.166969436
## [434,] 0.276189812 0.2376360404 -0.413656235 0.289565312 -0.222468724
## [435,] 1.057146615 -0.9098777867 0.418598301 0.091516686 0.072909388
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## [437,] 0.013654698 0.0184049756 0.103134336 0.193234213 0.166969436
## [438,] -0.195390698 -0.1127967791 0.027842652 -0.163889579 0.180188089
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## [440,] 0.052352326 0.7089579128 0.500452585 -0.095868421 -0.077265782
## [441,] -0.100614181 1.6148141499 -0.606285333 -0.185585675 0.713040991
## [442,] -0.261850249 -0.3814326845 -0.217032029 0.579464820 -0.102651990
## [443,] 1.178188310 -1.0620285349 -0.484306452 -0.201039278 -0.625448517
## [444,] 0.011851930 0.0873968673 0.097280007 0.152137423 0.282322781
## [445,] 0.253258739 0.0347866401 0.220025391 0.424254507 0.272234800
## [446,] -0.132815243 -0.1831821569 0.115102599 0.184735056 0.247558213
## [447,] 0.173765287 0.2797228181 0.441022687 -0.481570674 0.163725251
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## [449,] -0.478089716 -0.0187206366 -0.021890808 0.233753713 0.056151787
## [450,] -0.075191407 0.1703468699 -0.016837816 0.050304752 0.324667037
## [451,] 0.063053964 -0.5718350153 -0.178485853 -0.123261376 0.275166286
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## [453,] -0.541054102 0.1902343250 0.087992310 -0.273250133 0.247806525
## [454,] -0.075191407 0.1703468699 -0.016837816 0.050304752 0.324667037
## [455,] 0.040403867 0.0301497496 -0.044487928 -0.009153546 0.058067382
## [456,] 0.100344363 0.0230016217 -0.244722674 -0.394751960 -0.269638193
## [457,] -0.018312958 -0.0749414053 0.038268467 -0.089003293 0.440832090
## [458,] 0.319781131 0.2319904526 -0.291509645 -0.071373871 0.093033180
## [459,] -0.075191407 0.1703468699 -0.016837816 0.050304752 0.324667037
## [460,] 0.013654698 0.0184049756 0.103134336 0.193234213 0.166969436
## [461,] -0.048920758 0.0887903534 0.015874389 -0.155390421 0.099599312
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## [463,] -0.075191407 0.1703468699 -0.016837816 0.050304752 0.324667037
## [464,] 0.026944952 0.1290456739 -0.244998229 0.318330276 0.347050320
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## [468,] 0.459798216 0.1031638189 -0.466290166 -1.115445205 0.237500311
## [469,] 0.312395358 0.8244986136 -0.865624720 0.344442865 0.266633713
## [470,] 0.011851930 0.0873968673 0.097280007 0.152137423 0.282322781
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## [472,] 0.100344363 0.0230016217 -0.244722674 -0.394751960 -0.269638193
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## [475,] 0.213189203 0.4236966463 0.014156879 -0.297799192 0.538129814
## [476,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [477,] 0.603931282 -0.2898595424 0.525683679 0.507173653 -0.042659090
## [478,] 0.074073714 0.1045581382 -0.277434879 -0.189056787 -0.044570467
## [479,] 0.850173554 -0.4646764453 0.134466112 -0.297042296 0.289802252
## [480,] 0.031176928 -0.0793000610 0.549940292 -0.591668152 0.126469945
## [481,] 0.100344363 0.0230016217 -0.244722674 -0.394751960 -0.269638193
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## [483,] -0.061901152 0.2809875682 -0.364970381 0.175400814 0.504747922
## [484,] -0.117550435 -0.0007865872 0.040374971 -0.198187052 0.222639665
## [485,] -0.117550435 -0.0007865872 0.040374971 -0.198187052 0.222639665
## [486,] 0.090631379 -0.1451354783 -0.016376134 -0.175802417 0.162670813
## [487,] -0.117550435 -0.0007865872 0.040374971 -0.198187052 0.222639665
## [488,] -0.110234744 0.0061040082 0.181395517 -0.108425397 0.032241214
## [489,] -0.112717010 -0.1014343356 -0.059514155 -0.044993530 0.127094537
## [490,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [491,] 0.013478469 0.2889342090 0.255977601 -0.140242042 0.041607266
## [492,] -0.481482610 0.8090218513 1.261235533 0.930155411 -0.697643127
## [493,] 0.172897975 0.0936430665 -0.358358068 0.186277741 0.328698865
## [494,] 0.013654698 0.0184049756 0.103134336 0.193234213 0.166969436
## [495,] -0.071648137 0.3244205392 0.337930027 -0.010704483 0.182710095
## [496,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [497,] -0.028704331 -0.1527284815 0.160347123 -0.055257590 0.064942064
## [498,] 0.013654698 0.0184049756 0.103134336 0.193234213 0.166969436
## [499,] 0.100344363 0.0230016217 -0.244722674 -0.394751960 -0.269638193
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## [501,] 0.684512816 0.7870432033 0.109165054 -0.075379974 -0.077821730
## [502,] 0.276189812 0.2376360404 -0.413656235 0.289565312 -0.222468724
## [503,] 0.233830783 0.0665025833 -0.356443448 0.041073509 -0.324496096
## [504,] -0.043407833 0.1646728404 0.151040606 -0.106725557 0.024554206
## [505,] 0.136717315 0.0719797795 -0.296261017 -0.096076519 0.384275371
## [506,] 0.146166899 0.3166848330 -0.173427039 0.180122731 -0.157242422
## [507,] -0.013590171 0.3547403879 -0.094418470 -0.050007565 0.122683206
## [508,] 0.214013107 0.4439815825 0.425561227 0.088744533 0.091600255
## [509,] -0.104549110 0.1208864425 0.099244517 -0.424526606 -0.546065906
## [510,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [511,] -0.041605066 0.0956809488 0.156894935 -0.065628766 -0.090799140
## [512,] -0.075191407 0.1703468699 -0.016837816 0.050304752 0.324667037
## [513,] -0.112717010 -0.1014343356 -0.059514155 -0.044993530 0.127094537
## [514,] 0.375076716 0.1499179871 0.284211805 0.240277813 0.275110226
## [515,] 0.074073714 0.1045581382 -0.277434879 -0.189056787 -0.044570467
## [516,] -0.347751671 -0.3729240580 -0.054035199 -0.782738899 0.182179093
## [517,] -0.106062948 0.1788460028 -0.313611924 -0.114187780 0.518073895
## [518,] 0.238664209 -0.0341451650 -0.456332573 0.194267031 -0.420041224
## [519,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [520,] -0.114007166 0.1532870821 0.395142814 -0.259196287 0.080682723
## [521,] 0.293959793 -0.1162176306 0.119388877 0.505918715 -0.237964178
## [522,] -0.023870906 -0.2533762299 0.060457998 0.097935932 -0.030603065
## [523,] -0.025673673 -0.1843843382 0.054603668 0.056839141 0.084750281
## [524,] -0.117550435 -0.0007865872 0.040374971 -0.198187052 0.222639665
## [525,] 0.085797954 -0.0444877299 0.083512991 -0.328995939 0.258215941
## [526,] 0.015354140 -0.6793653738 0.180355895 -0.085868109 -0.302921402
## [527,] -0.048920758 0.0887903534 0.015874389 -0.155390421 0.099599312
## [528,] 0.076053924 0.2185488312 0.343237549 0.208382593 0.108977390
## [529,] -0.117550435 -0.0007865872 0.040374971 -0.198187052 0.222639665
## [530,] 0.132912568 0.1765593420 0.653054415 0.061585661 -0.004450364
## [531,] -0.028704331 -0.1527284815 0.160347123 -0.055257590 0.064942064
## [532,] -0.187958732 -0.0072668811 0.213942384 -0.259559890 0.228690770
## [533,] 0.119976012 0.4297652646 0.020120177 -0.001574219 -0.084500038
## [534,] 0.142703391 0.1941350788 -0.301935461 -0.146260157 -0.167610821
## [535,] 0.652538484 0.5117524133 1.477733818 0.203444390 0.278147188
## [536,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [537,] 0.047040059 -0.1394898905 -0.138522724 0.185136766 -0.152831092
## [538,] -0.558513674 -0.0315840654 -0.108444822 0.204942445 -0.025328584
## [539,] 0.176250068 0.4466110557 0.578324074 -0.544446634 0.312040339
## [540,] -0.048920758 0.0887903534 0.015874389 -0.155390421 0.099599312
## [541,] -0.189852556 0.0078847380 0.675592638 0.454913970 0.773877239
## [542,] 0.181722997 0.1391394293 -0.370429074 0.127633601 -0.097232290
## [543,] -0.132815243 -0.1831821569 0.115102599 0.184735056 0.247558213
## [544,] -0.114007166 0.1532870821 0.395142814 -0.259196287 0.080682723
## [545,] -0.028704331 -0.1527284815 0.160347123 -0.055257590 0.064942064
## [546,] -0.023870906 -0.2533762299 0.060457998 0.097935932 -0.030603065
## [547,] -0.023870906 -0.2533762299 0.060457998 0.097935932 -0.030603065
## [548,] 0.047040059 -0.1394898905 -0.138522724 0.185136766 -0.152831092
## [549,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [550,] -0.515615319 -0.2905018421 -0.064567147 0.138455431 -0.141420714
## [551,] -0.104286623 0.2315142082 -0.730899696 -0.341685652 -0.187674414
## [552,] -0.088249128 -0.1139989604 -0.032656279 -0.291785493 0.017380157
## [553,] -0.006233206 -0.0802898286 -0.229931251 -0.293436717 -0.190744969
## [554,] 0.782643735 -0.2658447380 0.204554063 -0.201923325 0.321428572
## [555,] 0.488843804 0.2860741635 -0.004981423 -0.342721964 -0.088365060
## [556,] -1.107198818 -0.4583799881 0.032531838 0.026108954 0.253763139
## [557,] 0.504590807 1.0182248727 -0.190816218 0.153241136 -0.040411922
## [558,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [559,] 0.042206634 -0.0388421421 -0.038633598 0.031943244 -0.057285963
## [560,] -0.702716917 -1.7229105046 0.715281188 -0.059063073 -1.325220143
## [561,] -0.025673673 -0.1843843382 0.054603668 0.056839141 0.084750281
## [562,] -0.028704331 -0.1527284815 0.160347123 -0.055257590 0.064942064
## [563,] 0.042206634 -0.0388421421 -0.038633598 0.031943244 -0.057285963
## [564,] 0.042206634 -0.0388421421 -0.038633598 0.031943244 -0.057285963
## [565,] 0.047040059 -0.1394898905 -0.138522724 0.185136766 -0.152831092
## [566,] -0.030507098 -0.0837365898 0.154492794 -0.096354381 0.180295409
## [567,] 0.183862193 -0.4001660660 -0.141374029 0.122134881 0.528723209
## [568,] 0.297031109 -0.1975986419 -0.538456548 -0.481727942 0.482656212
## [569,] -0.048920758 0.0887903534 0.015874389 -0.155390421 0.099599312
## [570,] 0.062886491 -0.2369496907 -0.088228857 0.051054313 0.009145310
## [571,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [572,] 0.110152125 0.0876770079 -0.361851849 -0.362177722 -0.286332730
## [573,] -0.431602640 -0.3417959880 0.155294131 0.128191370 -0.203573187
## [574,] -0.082426589 0.1086355860 0.017136235 0.138719642 0.105524993
## [575,] 0.013654698 0.0184049756 0.103134336 0.193234213 0.166969436
## [576,] -0.333983068 0.4275275144 -0.685519385 -0.227944589 0.228695307
## [577,] -0.703913367 -0.2830841121 0.065129096 -0.562406793 -0.311355028
## [578,] 0.004225624 0.6473253931 0.003165440 0.365062444 0.280898503
## [579,] 0.011851930 0.0873968673 0.097280007 0.152137423 0.282322781
## [580,] -0.301919420 -0.3822542138 0.406853338 0.113163482 0.247811312
## [581,] -0.028704331 -0.1527284815 0.160347123 -0.055257590 0.064942064
## [582,] -0.119353202 0.0682053045 0.034520641 -0.239283842 0.337993011
## [583,] 0.215733136 -0.2369945653 0.177349052 0.328956225 0.074662300
## [584,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [585,] 0.330847805 0.1719734812 -0.586006444 0.290303453 0.263682175
## [586,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [587,] 0.233830783 0.0665025833 -0.356443448 0.041073509 -0.324496096
## [588,] -0.117550435 -0.0007865872 0.040374971 -0.198187052 0.222639665
## [589,] -0.069251300 -0.7253786772 0.565577302 0.112133279 -0.078849768
## [590,] 0.216470951 0.2625029287 0.679584463 0.382270797 -0.131989980
## [591,] -0.096918666 0.1820271095 -0.041657232 0.818192307 0.939541656
## [592,] -0.067875715 0.1772374653 0.124182731 0.140066407 0.134268586
## [593,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [594,] -0.089760996 0.2335398812 -0.334016413 0.024078922 -0.250621478
## [595,] 0.013654698 0.0184049756 0.103134336 0.193234213 0.166969436
## [596,] 0.320922604 0.3692057471 0.281746346 0.413191055 -0.229537247
## [597,] -0.231725506 -0.6925620621 -0.048160559 0.405051694 -0.005359669
## [598,] 0.556323843 -0.2239612535 -0.395073663 -0.721974224 -0.159365928
## [599,] -0.051607939 0.3534309377 0.635246026 -0.244047908 0.022690677
## [600,] 0.077616983 0.2586318075 0.077332964 -0.250066022 -0.186527410
## [601,] 0.122053606 0.0155950774 0.157266025 0.032833242 0.327905030
## [602,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [603,] -0.117550435 -0.0007865872 0.040374971 -0.198187052 0.222639665
## [604,] -0.028704331 -0.1527284815 0.160347123 -0.055257590 0.064942064
## [605,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [606,] 0.663991270 -0.7295826979 0.248555609 -0.451874718 -0.127548681
## [607,] -0.203452989 0.0060321937 0.127728888 -0.239125193 0.167184321
## [608,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [609,] 0.170235510 -0.0404931607 -0.016442180 0.043634329 -0.392666520
## [610,] 0.340616832 0.2509172874 -0.207326894 -0.118839751 0.286838301
## [611,] -0.587716681 1.3289828782 -0.166842760 0.460192151 0.289491852
## [612,] 0.151037908 0.5153530039 0.763078326 -0.336884736 0.246836034
## [613,] -0.071648137 0.3244205392 0.337930027 -0.010704483 0.182710095
## [614,] -0.075191407 0.1703468699 -0.016837816 0.050304752 0.324667037
## [615,] 0.381051279 0.2536680901 -0.204941306 0.275612221 0.645589562
## [616,] -0.028704331 -0.1527284815 0.160347123 -0.055257590 0.064942064
## [617,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [618,] 0.176767069 0.0790276922 -0.807393521 -0.621780211 -0.199061481
## [619,] -0.048920758 0.0887903534 0.015874389 -0.155390421 0.099599312
## [620,] 0.063357946 0.0263734352 -0.007323977 -0.192547508 0.283441298
## [621,] 0.254225380 0.2183005845 -0.077754438 0.271110539 -0.475446715
## [622,] -0.094392946 -0.6807868318 -0.298978925 -0.149357752 0.299287847
## [623,] -0.075191407 0.1703468699 -0.016837816 0.050304752 0.324667037
## [624,] -0.132815243 -0.1831821569 0.115102599 0.184735056 0.247558213
## [625,] -0.221661347 -0.0312402626 -0.004869553 0.041805594 0.405255814
## [626,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [627,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [628,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [629,] -0.071648137 0.3244205392 0.337930027 -0.010704483 0.182710095
## [630,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [631,] 0.096053151 0.3119239050 -0.449833279 0.364434320 0.340175639
## [632,] -0.061904278 -0.0692958175 -0.083878122 0.271935891 0.125330186
## [633,] 0.495547434 -0.6874479743 -0.491905594 -0.528071270 -0.448169438
## [634,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [635,] 0.108328482 0.2414262182 -0.183197402 -0.260098390 -0.008825514
## [636,] -0.090973052 -0.1297885763 -0.374797900 0.148540149 0.203383698
## [637,] -0.431602640 -0.3417959880 0.155294131 0.128191370 -0.203573187
## [638,] -0.117550435 -0.0007865872 0.040374971 -0.198187052 0.222639665
## [639,] -0.086446361 -0.1829908521 -0.026801950 -0.250688703 -0.097973189
## [640,] -0.091279787 -0.0823431037 0.073087176 -0.403882225 -0.002428060
## [641,] -0.028704331 -0.1527284815 0.160347123 -0.055257590 0.064942064
## [642,] -0.635267655 -0.5300924080 -0.431246414 0.176224669 0.091112459
## [643,] -0.108839121 0.5025078882 -0.017726119 0.354479659 -0.284647366
## [644,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [645,] 0.042206634 -0.0388421421 -0.038633598 0.031943244 -0.057285963
## [646,] -0.112717010 -0.1014343356 -0.059514155 -0.044993530 0.127094537
## [647,] 0.281810675 -0.0224604775 0.078257456 0.262963538 0.047979402
## [648,] 0.281810675 -0.0224604775 0.078257456 0.262963538 0.047979402
## [649,] -0.237749727 -0.2839302362 0.085055439 -0.412381382 0.078160717
## [650,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [651,] 0.151243746 0.4463088512 0.005235050 0.255181900 0.158213281
## [652,] -0.086446361 -0.1829908521 -0.026801950 -0.250688703 -0.097973189
## [653,] 0.550525982 -0.2888334937 -0.265227253 -0.328080867 0.900721943
## [654,] 0.495701288 0.2609948977 0.933442094 0.118850532 0.160284309
## [655,] 0.556597484 0.7143959792 0.137175466 -0.354227417 -0.350654662
## [656,] -0.065840415 -0.0654595584 -0.233913968 -0.035830986 -0.108290756
## [657,] -0.109173740 0.0526393337 0.295253688 -0.106002765 -0.014862406
## [658,] 0.135852393 0.4719342408 0.259802565 0.066973485 0.022346905
## [659,] 0.042206634 -0.0388421421 -0.038633598 0.031943244 -0.057285963
## [660,] 0.037087297 0.1079299518 -0.040036182 0.013147665 0.508509024
## [661,] 0.040403867 0.0301497496 -0.044487928 -0.009153546 0.058067382
## [662,] 0.013654698 0.0184049756 0.103134336 0.193234213 0.166969436
## [663,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [664,] -0.071648137 0.3244205392 0.337930027 -0.010704483 0.182710095
## [665,] -0.124836421 0.6947689941 -0.236143201 0.017505659 -1.146550819
## [666,] -0.764468235 -0.0664689635 -0.162458995 -0.093336327 0.123383594
## [667,] -0.426769215 -0.4424437364 0.055405006 0.281384893 -0.299118315
## [668,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [669,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [670,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [671,] 0.084565663 0.1322913150 -0.095846385 0.280435048 0.044741409
## [672,] -0.106307035 0.0019905265 0.209191895 -0.289224004 -0.026624169
## [673,] -0.075191407 0.1703468699 -0.016837816 0.050304752 0.324667037
## [674,] -0.498380859 0.3535439711 -0.099871558 0.603651367 -0.042836580
## [675,] -0.061904278 -0.0692958175 -0.083878122 0.271935891 0.125330186
## [676,] -0.168457816 0.8423920070 0.440815993 -0.463548099 0.485333163
## [677,] -0.048920758 0.0887903534 0.015874389 -0.155390421 0.099599312
## [678,] 0.027506083 0.1590375866 0.188154237 -0.515695464 -0.116219994
## [679,] 0.056738949 -0.2534530209 -0.041697493 -0.286313257 -0.470247985
## [680,] -0.071648137 0.3244205392 0.337930027 -0.010704483 0.182710095
## [681,] -0.634813932 0.1193984778 0.024809098 0.586658623 -0.705833228
## [682,] -0.476955375 0.2110308048 -0.753006810 -0.325166516 -0.018335915
## [683,] 0.263563896 0.8078837253 -0.459568662 -0.748049933 0.175047539
## [,29] [,30] [,31] [,32]
## [1,] -0.1053899525 -0.221954475 0.0374261817 -0.0898273461
## [2,] -0.0751020225 -0.481565372 0.0776935703 0.2145103167
## [3,] -0.4015402900 0.203911264 -0.0665100485 0.1220074534
## [4,] -0.4173451286 -0.356796758 -0.3007207052 -0.0851070251
## [5,] 0.0032400817 0.435227366 0.1390762049 -0.2047073743
## [6,] -0.4948010198 0.272584182 -0.2738849352 -0.1873908052
## [7,] -0.1241490511 -0.232431729 0.0414691624 -0.0979506549
## [8,] -0.2512200926 -0.073287090 -0.3546910035 -0.4399262075
## [9,] -0.3810239802 0.204952836 -1.0275737592 0.2356592827
## [10,] 0.2818108005 0.063482097 0.1132852500 -0.0515562152
## [11,] 0.1325902764 -0.240058029 0.2995559584 0.2242427719
## [12,] -0.0257522848 0.214482653 -0.0754882177 -0.1240230785
## [13,] -0.1126024468 0.428034555 0.7547233699 0.4142078103
## [14,] -0.2661359017 -0.173009527 0.1417812491 -0.1207641047
## [15,] -0.7928804790 -0.290051504 -0.2814408549 0.1074637876
## [16,] 0.2474310824 -0.271810955 -0.5413026395 0.1470233583
## [17,] 0.2236790945 0.099295026 0.2797190025 -0.1014961284
## [18,] -0.0761610172 -0.070575249 0.1577961833 -0.2504835052
## [19,] -0.4642169371 -0.143970584 -0.7660059361 -0.0442084364
## [20,] -0.0296565433 -0.227837832 -0.0465038657 -0.0705726322
## [21,] 0.1016006543 -0.293457879 0.1698818714 0.0038952512
## [22,] 0.1762758808 0.863450486 0.0098311502 -1.0475972817
## [23,] -0.1784922599 0.031725017 0.2664498449 0.1311074192
## [24,] -0.2032290037 -0.283987564 0.0588755089 -0.0676506530
## [25,] -0.6906673019 0.385430162 0.2305488002 -0.3960389618
## [26,] 0.2154587262 0.039841623 0.3406965418 0.4729407571
## [27,] 0.1944501592 -0.052084200 0.1593490009 0.0591600307
## [28,] -0.0257522848 0.214482653 -0.0754882177 -0.1240230785
## [29,] -0.0974817587 -0.095339782 -0.0194266685 0.1292605073
## [30,] 0.1573270202 0.075654552 0.5071302944 0.4230008440
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## [683,] 0.1499127847BreastCancer_clean$NewScore <- mjca1$rowcoord[, 1] #dim1
head(BreastCancer_clean)## Id Cl.thickness Cell.size Cell.shape Marg.adhesion Epith.c.size
## 1 1000025 5 1 1 1 2
## 2 1002945 5 4 4 5 7
## 3 1015425 3 1 1 1 2
## 4 1016277 6 8 8 1 3
## 5 1017023 4 1 1 3 2
## 6 1017122 8 10 10 8 7
## Bare.nuclei Bl.cromatin Normal.nucleoli Mitoses Class NewScore
## 1 1 3 1 1 benign 0.8843631
## 2 10 3 2 1 benign -0.9870290
## 3 2 3 1 1 benign 0.8474861
## 4 4 3 7 1 benign -0.9310026
## 5 1 3 1 1 benign 0.7956928
## 6 10 9 7 1 malignant -2.1731476Now, let’s check whether the factors are independent
(Chi-Sq scores for significance of correlation - smaller the stronger is the fit/relationship and Cramer’s V for strength of it - the opposite. )
features1 <- cbind( BreastCancer_clean$Cell.size, BreastCancer_clean$Cell.shape )
chsq1<- chisq.test(features1)## Warning in chisq.test(features1): Chi-squared approximation may be
## incorrect#X-squared = 131.71, df = 682, p-value = 1. There is no relation
library(lsr)
crv1<- cramersV(features1)## Warning in chisq.test(...): Chi-squared approximation may be incorrect#0.1740442 : There is weak relations between Cell size and Cell shape
features2 <- cbind( BreastCancer_clean$Cell.size, BreastCancer_clean$Cl.thickness )
chsq2<- chisq.test(features2)## Warning in chisq.test(features2): Chi-squared approximation may be
## incorrect#X-squared = 538.53, df = 682, p-value = 1. There is no relation
crv2<- cramersV(features2)## Warning in chisq.test(...): Chi-squared approximation may be incorrect#0.3222482 : There is not strong relations between Cell size and Cell thickness
features3 <- cbind( BreastCancer_clean$Cell.size, BreastCancer_clean$Margin.adhesion )
chsq3<- chisq.test(features3)## Warning in chisq.test(features3): Chi-squared approximation may be
## incorrect#X-squared = 2033.6, df = 682, p-value < 2.2e-16. There might be some relation
crv3<- cramersV(features3)## Warning in chisq.test(...): Chi-squared approximation may be incorrect#0.03722366 : However, Cramer's scores tell us that that the relationship is not strong
features4 <- cbind( BreastCancer_clean$Cell.size, BreastCancer_clean$ Epith.c.size)
chsq4<- chisq.test(features4)## Warning in chisq.test(features4): Chi-squared approximation may be
## incorrect#X-squared = 329.42, df = 682, p-value = 1. No relation
crv4<- cramersV(features4)## Warning in chisq.test(...): Chi-squared approximation may be incorrect#0.2748433 : The relationship is not strong
# Creating table of statistical scores for features correaltion:
library(broom)
library(purrr)
ChiSq_table <- map_df(list(chsq1, chsq2, chsq3, chsq4), tidy)
#to get just the columns I need:
ChiSq_table[c("statistic", "p.value", "method")] ## # A tibble: 4 x 3
## statistic p.value method
## <dbl> <dbl> <chr>
## 1 132. 1.00e+ 0 Pearson's Chi-squared test
## 2 539. 10.00e- 1 Pearson's Chi-squared test
## 3 2034. 2.18e-134 Chi-squared test for given probabilities
## 4 329. 1.00e+ 0 Pearson's Chi-squared test# statistic is X-sq score. method is the dfWith chi-sq and Cramer’s V scores confirmed that the features we have on hands are not collinear. We can proceed for LR.
Saving MCA rowscore as a new feature in dataset. Splitting data. Building LR model on the train, testing it. Plotting ROC curve and interpreting AUC score.
# I will then use "NewScore" as one of the predictors for the model instead of original 9 variables.
#data(BreastCancer_clean)
#split into training and test set
train_size <- floor(0.75 * nrow(BreastCancer_clean))
set.seed(324)
train_Index <- sample(seq_len(nrow(BreastCancer_clean)), size = train_size)
train_classifier <- BreastCancer_clean[train_Index,]
test_classifier <- BreastCancer_clean[-train_Index,]
dim(train_classifier) #[512:12]## [1] 512 12dim(test_classifier) #[171:12]## [1] 171 12#Model:
MCA_glm <- glm(Class ~ NewScore, data = train_classifier, family = binomial)
summary(MCA_glm)##
## Call:
## glm(formula = Class ~ NewScore, family = binomial, data = train_classifier)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.96613 -0.09627 -0.06609 0.07182 2.02015
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.7990 0.3614 -4.978 6.44e-07 ***
## NewScore -4.0326 0.4462 -9.039 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 668.731 on 511 degrees of freedom
## Residual deviance: 86.263 on 510 degrees of freedom
## AIC: 90.263
##
## Number of Fisher Scoring iterations: 8#Intercept: -1.7990 NewScore -4.0326#Trying more elaborate LR with Control:
ctl_BRCA <- trainControl(method = "repeatedcv", repeats = 10,classProbs = T,
savePredictions = T)
#summary(ctrl_BRCA)
MCA_train <- train(Class ~ NewScore, data = train_classifier, method = "glm", family= "binomial", trControl = ctl_BRCA)
summary(MCA_train)##
## Call:
## NULL
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.96613 -0.09627 -0.06609 0.07182 2.02015
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.7990 0.3614 -4.978 6.44e-07 ***
## NewScore -4.0326 0.4462 -9.039 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 668.731 on 511 degrees of freedom
## Residual deviance: 86.263 on 510 degrees of freedom
## AIC: 90.263
##
## Number of Fisher Scoring iterations: 8#Intercept: -1.7990 NewScore -4.0326
# SAME RESULT!!!!Testing the model and evaluating its accuracy (ROC and AUC):
#Test set:
library(pROC)
MCA_glm_predicted <- predict(MCA_glm, newdata=test_classifier, type="response")
# Note: feed ROC not with vectors (predicted and actual) as here:
# roccurve <- roc(data=test_classifier, MCA_glm$Class, predicted_classification)
# But with a single matrix instead:
predicted_data <- data.frame(prob = MCA_glm_predicted,
class = test_classifier$Class)
roccurve <- roc(data = predicted_data, response = "class", "prob" ) ## Setting levels: control = benign, case = malignant## Setting direction: controls < cases# roc() calculates confusion matrix for test set and outputs AUC score
#another option is to use confusionMatrix()
plot(roccurve) # evaluation of a model performance on test to evaluate how well NewScore can predict malignancy state(=1) of breast cancer
#auc(roccurve)Both the ROC curve and the high AUC value (Area Under the Curve) indicate that the model is good in predicting no DM (i.e. true positives).
Vizualizing the results:
! Checking if log odds and independent variables are linearly correlated
# To convert from a probability to odds, divide the probability by one minus that probability. So if the probability is 10% or 0.10 , then the odds are 0.1/0.9 or ‘10%/90%’ or 1 out of 9
prediction_odds <- MCA_glm_predicted / (1 - MCA_glm_predicted)
log_prediction_odds <- log(prediction_odds)
#log_odds and indep.variable X must be linearly correlated:
cor.test(log_prediction_odds, test_classifier$NewScore)##
## Pearson's product-moment correlation
##
## data: log_prediction_odds and test_classifier$NewScore
## t = -Inf, df = 169, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -1 -1
## sample estimates:
## cor
## -1plot(log_prediction_odds, test_classifier$NewScore)
# Yes, they are correlated!plotting predicted vs actual obs.
#prepare df to plot = predicted + actual labels:
df_to_plot_results <- data.frame(Class_pred = MCA_glm_predicted, MCA_selected_features = test_classifier$NewScore,
classes = test_classifier$Class)
#Stash away actual labels as logical vector:
df_to_plot_results$Class <- as.numeric(test_classifier$Class) -1
# Plotting predictions and actual observations:
ggplot(data = df_to_plot_results) +
geom_point(aes(x=MCA_selected_features, y = Class)) +
geom_line(aes(x = MCA_selected_features, y = Class_pred, col = "Blue")) +
geom_line(aes(x = MCA_selected_features, y = 1-Class_pred, col = "Red"))+
#(x and y whatever you name it, input data is the only thing to worry here.)
ggtitle("Probabilities for classifying whether benign or malignant")
CONCLUSION on MCA and Logistic Regression:
" > roccurve
Call: roc.data.frame(data = predicted_data, response = “class”, predictor = “prob”)
Data: prob in 116 controls (class benign) < 55 cases (class malignant). Area under the curve: 0.9892 "
Conclusion 1: Selected single Dim1 was a successful choice to select features for Logistic Regression. The model performed with TP of 98% on validation set, which is pretty high.
Conclusion 2. What could be done more: 1. Evaluation of the model right after building it.
The other ways to go about the task: 1. as.numeric(data) -> PCA -> Logistic Regression 2. kNN 3. data[-Class] -> k-Means with k=2 and also choosing k through silhouette analysis. It will be interesting to compare these results. Will do it when bit later.
The end. Thank you!
===================
Optional- exploring other packages to perform exactly same steps as before:
MCA performed with FactoMineR::MCA
library(FactoMineR)
library(factoextra)
res.mca <- MCA(BreastCancer_MCA, graph = T)
print(res.mca)## **Results of the Multiple Correspondence Analysis (MCA)**
## The analysis was performed on 683 individuals, described by 9 variables
## *The results are available in the following objects:
##
## name description
## 1 "$eig" "eigenvalues"
## 2 "$var" "results for the variables"
## 3 "$var$coord" "coord. of the categories"
## 4 "$var$cos2" "cos2 for the categories"
## 5 "$var$contrib" "contributions of the categories"
## 6 "$var$v.test" "v-test for the categories"
## 7 "$ind" "results for the individuals"
## 8 "$ind$coord" "coord. for the individuals"
## 9 "$ind$cos2" "cos2 for the individuals"
## 10 "$ind$contrib" "contributions of the individuals"
## 11 "$call" "intermediate results"
## 12 "$call$marge.col" "weights of columns"
## 13 "$call$marge.li" "weights of rows"#Other way:
#mca_output <- MCA(BreastCancer_MCA, ncp=2, ind.sup = NULL, quanti.sup = NULL, quali.sup = NULL, excl=NULL, graph = TRUE, level.ventil = 0, axes = c(1,2), row.w = NULL, method="Indicator", na.method="NA", tab.disj=NULL)
#summary(mca_output)Summary of MCA outputs with FactoMineR::summary.MCA().
Arguments: object: an object of class MCA nb.dec: number of decimal printed nbelements: number of row/column variables to be written. To have all the elements, use nbelements = Inf. ncp: Number of dimensions to be printed
Print the summary of the MCA for the dimensions 1 and 2:
MCA_summary<- summary(res.mca, nb.dec = 2, ncp = 2)##
## Call:
## MCA(X = BreastCancer_MCA, graph = T)
##
##
## Eigenvalues
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6 Dim.7
## Variance 0.72 0.31 0.23 0.21 0.20 0.20 0.19
## % of var. 8.11 3.51 2.62 2.37 2.30 2.24 2.16
## Cumulative % of var. 8.11 11.62 14.24 16.60 18.90 21.15 23.30
## Dim.8 Dim.9 Dim.10 Dim.11 Dim.12 Dim.13 Dim.14
## Variance 0.19 0.18 0.18 0.17 0.17 0.17 0.16
## % of var. 2.10 2.07 2.02 1.95 1.90 1.88 1.81
## Cumulative % of var. 25.41 27.48 29.49 31.44 33.34 35.22 37.03
## Dim.15 Dim.16 Dim.17 Dim.18 Dim.19 Dim.20 Dim.21
## Variance 0.16 0.16 0.15 0.15 0.14 0.14 0.14
## % of var. 1.76 1.75 1.68 1.66 1.63 1.61 1.58
## Cumulative % of var. 38.79 40.54 42.23 43.89 45.52 47.12 48.71
## Dim.22 Dim.23 Dim.24 Dim.25 Dim.26 Dim.27 Dim.28
## Variance 0.14 0.13 0.13 0.13 0.13 0.12 0.12
## % of var. 1.56 1.51 1.48 1.46 1.41 1.39 1.37
## Cumulative % of var. 50.27 51.78 53.26 54.72 56.13 57.51 58.89
## Dim.29 Dim.30 Dim.31 Dim.32 Dim.33 Dim.34 Dim.35
## Variance 0.12 0.12 0.12 0.12 0.11 0.11 0.11
## % of var. 1.35 1.33 1.32 1.30 1.29 1.23 1.21
## Cumulative % of var. 60.23 61.56 62.88 64.19 65.48 66.70 67.91
## Dim.36 Dim.37 Dim.38 Dim.39 Dim.40 Dim.41 Dim.42
## Variance 0.11 0.11 0.10 0.10 0.10 0.10 0.09
## % of var. 1.20 1.19 1.16 1.12 1.11 1.08 1.06
## Cumulative % of var. 69.11 70.30 71.46 72.57 73.68 74.76 75.82
## Dim.43 Dim.44 Dim.45 Dim.46 Dim.47 Dim.48 Dim.49
## Variance 0.09 0.09 0.09 0.09 0.09 0.09 0.08
## % of var. 1.05 1.03 1.02 1.00 0.98 0.96 0.94
## Cumulative % of var. 76.87 77.90 78.92 79.91 80.89 81.85 82.80
## Dim.50 Dim.51 Dim.52 Dim.53 Dim.54 Dim.55 Dim.56
## Variance 0.08 0.08 0.08 0.08 0.07 0.07 0.07
## % of var. 0.92 0.90 0.88 0.84 0.79 0.77 0.76
## Cumulative % of var. 83.71 84.62 85.50 86.34 87.13 87.90 88.66
## Dim.57 Dim.58 Dim.59 Dim.60 Dim.61 Dim.62 Dim.63
## Variance 0.07 0.06 0.06 0.06 0.06 0.06 0.05
## % of var. 0.74 0.73 0.69 0.68 0.66 0.64 0.62
## Cumulative % of var. 89.41 90.14 90.83 91.51 92.17 92.81 93.43
## Dim.64 Dim.65 Dim.66 Dim.67 Dim.68 Dim.69 Dim.70
## Variance 0.05 0.05 0.05 0.05 0.04 0.04 0.04
## % of var. 0.60 0.58 0.56 0.53 0.50 0.49 0.46
## Cumulative % of var. 94.02 94.60 95.16 95.69 96.19 96.68 97.13
## Dim.71 Dim.72 Dim.73 Dim.74 Dim.75 Dim.76 Dim.77
## Variance 0.04 0.04 0.03 0.03 0.03 0.02 0.02
## % of var. 0.44 0.41 0.39 0.33 0.31 0.27 0.24
## Cumulative % of var. 97.58 97.99 98.38 98.71 99.01 99.28 99.52
## Dim.78 Dim.79 Dim.80
## Variance 0.02 0.02 0.01
## % of var. 0.21 0.19 0.07
## Cumulative % of var. 99.73 99.93 100.00
##
## Individuals (the 10 first)
## Dim.1 ctr cos2 Dim.2 ctr cos2
## 1 | -0.61 0.07 0.27 | -0.09 0.00 0.01 |
## 2 | 0.68 0.09 0.03 | 0.57 0.15 0.02 |
## 3 | -0.58 0.07 0.09 | -0.04 0.00 0.00 |
## 4 | 0.64 0.08 0.02 | 0.26 0.03 0.00 |
## 5 | -0.55 0.06 0.10 | 0.00 0.00 0.00 |
## 6 | 1.49 0.45 0.09 | -1.08 0.54 0.05 |
## 7 | -0.45 0.04 0.12 | -0.10 0.00 0.01 |
## 8 | -0.65 0.08 0.12 | -0.01 0.00 0.00 |
## 9 | -0.58 0.07 0.02 | -0.43 0.09 0.01 |
## 10 | -0.68 0.09 0.14 | -0.02 0.00 0.00 |
##
## Categories (the 10 first)
## Dim.1 ctr cos2 v.test Dim.2 ctr cos2
## Cl.thickness_1 | -0.76 1.83 0.15 -10.08 | -0.19 0.27 0.01
## Cl.thickness_2 | -0.65 0.47 0.03 -4.76 | -0.05 0.01 0.00
## Cl.thickness_3 | -0.50 0.58 0.04 -5.48 | 0.12 0.08 0.00
## Cl.thickness_4 | -0.45 0.35 0.03 -4.21 | 0.06 0.01 0.00
## Cl.thickness_5 | 0.05 0.01 0.00 0.67 | 0.00 0.00 0.00
## Cl.thickness_6 | 0.69 0.36 0.02 4.09 | -0.21 0.07 0.00
## Cl.thickness_7 | 1.28 0.85 0.06 6.22 | 1.44 2.50 0.07
## Cl.thickness_8 | 1.29 1.65 0.11 8.84 | 0.05 0.01 0.00
## Cl.thickness_9 | 1.35 0.57 0.04 5.09 | -0.83 0.50 0.01
## Cl.thickness_10 | 1.31 2.68 0.19 11.49 | -0.06 0.01 0.00
## v.test
## Cl.thickness_1 -2.57 |
## Cl.thickness_2 -0.38 |
## Cl.thickness_3 1.30 |
## Cl.thickness_4 0.56 |
## Cl.thickness_5 -0.01 |
## Cl.thickness_6 -1.21 |
## Cl.thickness_7 7.04 |
## Cl.thickness_8 0.38 |
## Cl.thickness_9 -3.14 |
## Cl.thickness_10 -0.55 |
##
## Categorical variables (eta2)
## Dim.1 Dim.2
## Cl.thickness | 0.61 0.10 |
## Cell.size | 0.90 0.64 |
## Cell.shape | 0.86 0.62 |
## Marg.adhesion | 0.71 0.26 |
## Epith.c.size | 0.79 0.34 |
## Bare.nuclei | 0.75 0.07 |
## Bl.cromatin | 0.76 0.28 |
## Normal.nucleoli | 0.73 0.26 |
## Mitoses | 0.38 0.23 |#loading_score<- MCA_summary$CategoricalVariables_(eta2)[, 1]Note: For exporting the summary to a file, use the code: summary(res.mca, file =“myfile.txt”) For displaying the summary of more than 10 elements, use the argument nbelements in the function summary()
####Interpretation of MCA outputs (http://www.sthda.com/english/articles/31-principal-component-methods-in-r-practical-guide/113-ca-correspondence-analysis-in-r-essentials/)
Eigenvalues/variances and screeplot The proportion of variances retained by the different dimensions (axes) can be extracted using the function get_eigenvalue() [in factoextra] as follow :
eigenvalues <- get_eigenvalue(res.mca)
head(round(eigenvalues, 2))## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 0.72 8.11 8.11
## Dim.2 0.31 3.51 11.62
## Dim.3 0.23 2.62 14.24
## Dim.4 0.21 2.37 16.60
## Dim.5 0.20 2.30 18.90
## Dim.6 0.20 2.24 21.15SCREEPLOT factoextra::fviz_screeplot() (the percentages of inertia explained by the MCA dimensions):
fviz_screeplot(res.mca)
# It is possible that the two dimensions we chose are sufficient to explain data varianceMCA SCATTER plot: (Biplot of observ. and variable factors linked together) FactoMineR::plot.MCA()
# a simple format:
plot.MCA(res.mca)#, axes = c(1,2), choix=c("ind", "var"))
#plot(res.mca)Note: x : An object of class MCA axes : A numeric vector of length 2 specifying the component to plot choix : The graph to be plotted. Possible values are “ind” for the individuals and “var” for the variables
same MCA BIPLOT with different package: factoextra::fviz_mca_biplot():
fviz_mca_biplot(res.mca)
# Change the theme
#fviz_mca_biplot(res.mca) +
# theme_minimal()CONCLUSION ON BIPLOT: a global pattern within the data: rows (individuals) are represented by blue points and columns (variable categories) by red triangles. The distance between any row points or column points gives a measure of their similarity (or dissimilarity). Row points with similar profile are closed on the factor map. The same holds true for column points.
VARIABLE CATEGORIES
factoextra::get_mca_var() used to extract the results for variable categories. vs ca::mjca$rowcoord or $rowpcoord Output is a list containing the coordinates, the cos2 and the contribution of variable categories.
var <- get_mca_var(res.mca)
var## Multiple Correspondence Analysis Results for variables
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for categories"
## 2 "$cos2" "Cos2 for categories"
## 3 "$contrib" "contributions of categories"Variables can be visualized:
plot(res.mca, choix = "var")
Cell.size and Cell.shape are correlated to both dimensions.
There is no given variable strongly correlated only to dim.2 alone…
The coordinates are the squared correlations between variables and the dimensions.
However, we need to investigate more.
Extracting Coordinates of variable categories to be used a s new predictors in model:
head(round(var$coord, 2))## Dim 1 Dim 2 Dim 3 Dim 4 Dim 5
## Cl.thickness_1 -0.76 -0.19 0.17 -0.05 -0.13
## Cl.thickness_2 -0.65 -0.05 0.12 0.02 -0.33
## Cl.thickness_3 -0.50 0.12 0.01 -0.06 -0.01
## Cl.thickness_4 -0.45 0.06 0.15 0.01 0.31
## Cl.thickness_5 0.05 0.00 -0.34 -0.04 -0.02
## Cl.thickness_6 0.69 -0.21 0.36 0.52 -0.42visualize only variable categories: (factoextra::fviz_mca_var())
# Default plot
#fviz_mca_var(res.mca)
fviz_mca_var(res.mca, col.var="black", shape.var = 70)
MEASURING CONTRIBUTION of variable categories (%) to the dimensions
head(round(var$contrib,2))## Dim 1 Dim 2 Dim 3 Dim 4 Dim 5
## Cl.thickness_1 1.83 0.27 0.28 0.02 0.18
## Cl.thickness_2 0.47 0.01 0.05 0.00 0.44
## Cl.thickness_3 0.58 0.08 0.00 0.03 0.00
## Cl.thickness_4 0.35 0.01 0.12 0.00 0.60
## Cl.thickness_5 0.01 0.00 1.03 0.02 0.01
## Cl.thickness_6 0.36 0.07 0.30 0.70 0.47The variable categories with the larger value, contribute the most to the definition of the dimensions.
The different categories in the table are:
categories <- rownames(var$coord)
length(categories)## [1] 89there are initial 89 categories in our data.
HIGHLIGHTs on MOST CONTR-G VAR-S for each dimension:
#install.packages("corrplot")
library("corrplot")## corrplot 0.84 loadedhead(corrplot(var$contrib, is.corr = FALSE))
## Dim 1 Dim 2 Dim 3 Dim 4
## Cl.thickness_1 0.1378117042 0.0207148626 2.127337e-02 1.869176e-03
## Cl.thickness_2 0.0357631253 0.0005350944 3.990319e-03 1.017286e-04
## Cl.thickness_3 0.0434030398 0.0056765779 2.574009e-05 2.167341e-03
## Cl.thickness_4 0.0267095347 0.0011044249 9.370846e-03 2.942556e-05
## Cl.thickness_5 0.0006165451 0.0000000000 7.779277e-02 1.475081e-03
## Cl.thickness_6 0.0270696589 0.0055143641 2.237007e-02 5.249592e-02
## Dim 5
## Cl.thickness_1 0.0133554483
## Cl.thickness_2 0.0329050392
## Cl.thickness_3 0.0001171677
## Cl.thickness_4 0.0453055616
## Cl.thickness_5 0.0003907063
## Cl.thickness_6 0.0353811895Bar plot of variable contributions: (factoextra::fviz_contrib())
# Contributions of variables on Dim.1
fviz_contrib(res.mca, choice = "var", axes = 1)
If the contribution of variable categories were uniform, the expected value would be 1/number_of_categories = 1/22 = 4.5%.
The red dashed line on the graph above indicates the expected average contribution. For a given dimension, any category with a contribution larger than this threshold could be considered as important in contributing to that dimension.
It can be seen that the categories … are the most important in the definition of the first dimension.
# Contributions of rows on Dim.2
fviz_contrib(res.mca, choice = "var", axes = 2)
Correlation between variables and principal dimensions
# Total contribution on Dim.1 and Dim.2
fviz_contrib(res.mca, choice = "var", axes = 1:2)
The total contribution of a category, on explaining the variations retained by Dim.1 and Dim.2, is calculated as follow : (C1 * Eig1) + (C2 * Eig2).
C1 and C2 are the contributions of the category to dimensions 1 and 2, respectively. Eig1 and Eig2 are the eigenvalues of dimensions 1 and 2, respectively.
The expected average contribution of a category for Dim.1 and Dim.2 is : (4.5 * Eig1) + (4.5 * Eig2) = (4.50.34) + (4.50.13) = 2.12%
If data contains many categories, the TOP CONTR-ING categories
fviz_contrib(res.mca, choice = "var", axes = 1, top = 10)
fviz_contrib(res.mca, choice = "var", axes = 1:2, top = 10)
#####CONCLUSION:
According to the categories contribution barplot, Cell.size, Cell.shape, Normal.nucleoli, Bare.nuclei, Marg.adhesion and Epith.c.size_2 will be included in Logistic Regression with their factors.
#Optional:
#A second option is to draw a SCATTERPLOT of categories and to highlight categories according to the amount of their contributions.
# Control category point colors using their contribution
# Possible values for the argument col.row are :
# "cos2", "contrib", "coord", "x", "y"
fviz_mca_var(res.mca, col.var = "contrib")+
scale_color_gradient2(low="white", mid="blue",
high="red", midpoint=2)+theme_minimal()
# Optional:
#TRANSPARENCY BY CONTRIB.
#fviz_mca_var(res.mca, alpha.var="contrib")+
#theme_minimal()#Optional:
# TOP 10 contributing categories
fviz_mca_var(res.mca, select.var=list(contrib=10))
#Optional:
#Change individual colors by groups using the levels of the variable sick. The argument with factors and subfactors desired ='habillage':
#fviz_mca_ind(res.mca, label = "none", Cell.size=10)
#Add ellipses of point concentrations : the argument habillage is used to specify the factor variable for coloring the observations by groups.
#fviz_mca_ind(res.mca, label="none", Cell.shape=10,
# addEllipses = TRUE, ellipse.level = 0.95)#Optional:
#top 5 contributing individuals and variable categories
fviz_mca_biplot(res.mca, select.ind = list(contrib = 5),
select.var = list(contrib = 5)) +
theme_minimal()
#Supplementary individuals/variable categories are not shown because they don’t contribute to the construction of the axes.# Extracting coordinates for MCA individuals/observations:
coord = fviz_mca_ind(res.mca, select.ind = list(contrib = 10))+
theme_minimal()
coord
References: https://sebastianraschka.com/Articles/2014_python_lda.html
https://machinelearningmastery.com/linear-discriminant-analysis-for-machine-learning/ , https://sebastianraschka.com/Articles/2014_python_lda.html
Other cool sites: https://www.countbayesie.com/blog/2019/6/12/logistic-regression-from-bayes-theorem https://colah.github.io/posts/2014-03-NN-Manifolds-Topology/